First, calculate the number of contractual employees: 30% of 450 = 0.30 * 450 = 135 employees. Next, calculate the number of permanent employees: 40% of 450 = 0.40 * 450 = 180 employees. The total percentage of contractual and permanent employees is 30% + 40% = 70%. Therefore, the percentage of probationary employees is 100% - 70% = 30%. The number of probationary employees is 30% of 450 = 0.30 * 450 = 135 employees.

The ratio of successful to unsuccessful examinees is 3:5. This means for every 3 successful examinees, there are 5 unsuccessful ones. The total parts in the ratio are 3 + 5 = 8 parts. If 8 parts represent 2,400 individuals, then one part represents 2,400 / 8 = 300 individuals. The number of successful examinees is represented by 3 parts, so 3 * 300 = 900 successful examinees.

To find the average, sum all the values and divide by the number of values. Sum = 38 + 45 + 52 + 30 + 40 = 205. Number of days = 5. Average = 205 / 5 = 41 documents per day.

First, find the rate per encoder per hour. The total work done is 1,200 records by 5 encoders in 8 hours, which is 5 * 8 = 40 'encoder-hours'. So, the rate is 1,200 records / 40 encoder-hours = 30 records per encoder per hour. Now, for 3 data encoders working for 4 hours, the total 'encoder-hours' is 3 * 4 = 12 encoder-hours. The total records they can input is 12 encoder-hours * 30 records/encoder-hour = 360 records.

Cost for materials = (1/3) * Php 72,000 = Php 24,000. Cost for labor = (1/4) * Php 72,000 = Php 18,000. Total spent on materials and labor = Php 24,000 + Php 18,000 = Php 42,000. The remaining amount for administrative costs = Total budget - (Materials + Labor) = Php 72,000 - Php 42,000 = Php 30,000.

First, find the absolute increase: 300 - 250 = 50 applicants. To find the percentage increase, divide the increase by the original number of applicants and multiply by 100. Percentage increase = (50 / 250) * 100 = (1/5) * 100 = 20%.

To fence the property, you need to find its perimeter. The perimeter of a rectangle is 2 * (length + width). Perimeter = 2 * (60 m + 45 m) = 2 * 105 m = 210 meters. The total cost of fencing is the perimeter multiplied by the cost per meter. Total cost = 210 meters * Php 150/meter = Php 31,500.

The formula for time is Distance / Speed. Time = 360 km / 80 km/h = 4.5 hours.

First, apply the 10% discount: Discount amount = 0.10 * Php 25,000 = Php 2,500. Price after first discount = Php 25,000 - Php 2,500 = Php 22,500. Next, apply the additional 5% discount to the new price: Second discount amount = 0.05 * Php 22,500 = Php 1,125. Final price = Php 22,500 - Php 1,125 = Php 21,375.

Simple Interest (I) = Principal (P) * Rate (R) * Time (T). I = Php 50,000 * 0.06 * 3 = Php 9,000. The total amount to pay back is the Principal + Simple Interest. Total amount = Php 50,000 + Php 9,000 = Php 59,000.

First, convert 2 hours to minutes: 2 hours * 60 minutes/hour = 120 minutes. Next, find the printing rate per minute: 2,400 pages / 30 minutes = 80 pages/minute. Finally, calculate the total pages printed in 120 minutes: 80 pages/minute * 120 minutes = 9,600 pages.

This is a weighted average problem. Multiply each score by its corresponding percentage (as a decimal) and sum the results. Average score = (0.60 * 4) + (0.30 * 3) + (0.10 * 1) = 2.4 + 0.9 + 0.1 = 3.4.

Let the age of the younger colleague be 'x'. Then the age of the older colleague is 'x + 8'. The sum of their ages is 72, so x + (x + 8) = 72. This simplifies to 2x + 8 = 72. Subtract 8 from both sides: 2x = 64. Divide by 2: x = 32. So, the younger colleague is 32 years old.

First, calculate the total volume (capacity) of the tank. Volume of a rectangular prism = Length * Width * Height = 5 m * 3 m * 2 m = 30 cubic meters. The tank is filled to 3/4 of its capacity, so the volume of water is (3/4) * 30 cubic meters = 22.5 cubic meters.

Observe the differences between consecutive numbers: 11 - 7 = 4, 16 - 11 = 5, 22 - 16 = 6, 29 - 22 = 7. The differences are increasing by 1 each time (4, 5, 6, 7). Therefore, the next difference should be 8. So, the next number in the sequence is 29 + 8 = 37.

Total cost of rice = Php 4,800. Revenue from the first batch: 100 kg * Php 35/kg = Php 3,500. Revenue from the remaining batch: 50 kg * Php 30/kg = Php 1,500. Total revenue = Php 3,500 + Php 1,500 = Php 5,000. Profit/Loss = Total Revenue - Total Cost = Php 5,000 - Php 4,800 = Php 200. Since the result is positive, it's a profit.

Let M be the number of motorcycles and C be the number of cars. We have two equations: 1) M + C = 65 (total vehicles), 2) 2M + 4C = 210 (total wheels). From equation 1, M = 65 - C. Substitute this into equation 2: 2(65 - C) + 4C = 210. Simplify: 130 - 2C + 4C = 210. Combine like terms: 130 + 2C = 210. Subtract 130 from both sides: 2C = 80. Divide by 2: C = 40. So, there are 40 cars.

First, calculate the total percentage of deductions: 15% (taxes) + 5% (health insurance) = 20%. Next, calculate the total deduction amount: 20% of Php 32,500 = 0.20 * Php 32,500 = Php 6,500. Finally, subtract the total deductions from the gross salary to find the net salary: Php 32,500 - Php 6,500 = Php 26,000.

The total number of ratio parts is 2 + 3 + 4 = 9 parts. The value of one part is the total bonus divided by the total parts: Php 18,000 / 9 = Php 2,000. Employee B receives 3 parts, so Employee B will receive 3 * Php 2,000 = Php 6,000.

For a square, the perimeter is 4 times the length of one side (P = 4s). Given the perimeter is 48 meters, the side length (s) = 48 meters / 4 = 12 meters. The area of a square is side * side (A = s^2). Area = 12 meters * 12 meters = 144 square meters.

Let 'D' be the number of dengue cases in December. January's cases were 20% more than December's, which means January's cases are 100% + 20% = 120% of December's cases. So, 1.20 * D = 120. To find D, divide 120 by 1.20: D = 120 / 1.20 = 100 cases. Therefore, 100 dengue cases were recorded in December.

First, calculate the funding for infrastructure development: (5/8) * Php 1,200,000 = Php 750,000. Next, find the remaining funds: Php 1,200,000 - Php 750,000 = Php 450,000. Finally, calculate the allocation for personnel salaries, which is 1/3 of the remaining funds: (1/3) * Php 450,000 = Php 150,000.

Employee A's rate is 1/10 of the task per hour. Employee B's rate is 1/15 of the task per hour. When they work together, their rates add up: (1/10) + (1/15) = (3/30) + (2/30) = 5/30 = 1/6 of the task per hour. If they complete 1/6 of the task per hour, they will complete the entire task (1 whole task) in 1 / (1/6) = 6 hours.

To find when they will next be at the terminal together, we need to find the Least Common Multiple (LCM) of their return intervals (45 minutes and 60 minutes). Prime factorization of 45 = 3^2 * 5. Prime factorization of 60 = 2^2 * 3 * 5. LCM(45, 60) = 2^2 * 3^2 * 5 = 4 * 9 * 5 = 180 minutes. 180 minutes is equal to 3 hours. Since they both left at 6:00 AM, they will next be at the terminal together 3 hours later, which is 9:00 AM.

First, calculate the total number of pens in the bag: 8 (red) + 5 (blue) + 7 (black) = 20 pens. The number of blue pens is 5. Probability is calculated as (Number of favorable outcomes) / (Total number of possible outcomes). So, the probability of drawing a blue pen is 5/20, which simplifies to 1/4.

Let 'S' be the original monthly salary. A 15% increase means the new salary is 100% + 15% = 115% of the original salary. So, 1.15 * S = Php 28,750. To find S, divide the new salary by 1.15: S = Php 28,750 / 1.15 = Php 25,000.

To find the amount of pure acid, multiply the total volume of the solution by the percentage of acid. Amount of pure acid = 30% of 20 liters = 0.30 * 20 = 6 liters.

This is a geometric progression where each term is obtained by multiplying the previous term by 3. 3 * 3 = 9, 9 * 3 = 27. So, the missing number is 27 * 3 = 81. To verify, 81 * 3 = 243.

First, convert all proportions to fractions or decimals. 0.4 as a fraction is 4/10, which simplifies to 2/5. So, fiction books are 2/5 of the total. Reference books are 1/5 of the total. Total fraction of fiction and reference books = 2/5 + 1/5 = 3/5. The remaining books are non-fiction, so 1 (whole) - 3/5 = 2/5 of the books are non-fiction.

Number of days remaining in March (March has 31 days): 31 - 15 = 16 days. Remaining days for the project: 75 - 16 = 59 days. April has 30 days. Subtract April's days from the remaining: 59 - 30 = 29 days. These 29 days will fall in May. So, the project is expected to be completed on May 29, 2023.

Let the number of male employees be 7x and female employees be 5x. The difference in their numbers is 7x - 5x = 2x. We are given that this difference is 24, so 2x = 24. Dividing by 2, we get x = 12. Number of male employees = 7 * 12 = 84. Number of female employees = 5 * 12 = 60. Total number of employees = 84 + 60 = 144.

Follow the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). First, Exponents: 5^2 = 25. Next, Division: 18 / 3 = 6. Next, Multiplication: 2 * 4 = 8. Now substitute these values back into the expression: 25 + 6 - 8. Perform Addition: 25 + 6 = 31. Perform Subtraction: 31 - 8 = 23.

This is a percentage of a percentage calculation. We need to find 25% of the 60% of employees. Convert percentages to decimals: 0.25 * 0.60 = 0.15. Convert back to percentage: 0.15 * 100% = 15%. So, 15% of the total employees expressed interest in additional health programs.

To find the median, first arrange the bids in ascending order: Php 110,000, Php 115,000, Php 120,000, Php 125,000, Php 130,000, Php 135,000, Php 140,000. Since there are 7 bids (an odd number), the median is the middle value. In a set of 7 values, the 4th value is the median. The 4th value in the ordered list is Php 125,000.

Supplementary angles are two angles whose sum is 180 degrees. If one angle measures 75 degrees, then the other angle measures 180 degrees - 75 degrees = 105 degrees.

By 9:00 AM, the first courier has traveled for 1 hour (from 8:00 AM to 9:00 AM) at a speed of 50 km/h. So, the first courier is 50 km away from the office. The second courier starts at 9:00 AM. The relative speed at which the second courier closes the gap on the first courier is the difference in their speeds: 75 km/h - 50 km/h = 25 km/h. The time it will take for the second courier to cover the 50 km lead of the first courier is Distance / Relative Speed = 50 km / 25 km/h = 2 hours. Since the second courier started at 9:00 AM, they will overtake the first courier 2 hours later, which is 11:00 AM.

The area of a circle is given by the formula A = pi * r^2, where r is the radius. Given radius r = 7 meters and pi = 22/7. Area = (22/7) * (7 meters)^2 = (22/7) * 49 square meters. Area = 22 * (49/7) square meters = 22 * 7 square meters = 154 square meters.

Let the smallest even integer be 'x'. Since they are consecutive even integers, the next two would be 'x + 2' and 'x + 4'. Their sum is 108: x + (x + 2) + (x + 4) = 108. Combine like terms: 3x + 6 = 108. Subtract 6 from both sides: 3x = 102. Divide by 3: x = 34. The smallest integer is 34. (The integers are 34, 36, 38).

First, calculate the price after the 10% discount: Discount amount = 0.10 * Php 30,000 = Php 3,000. Discounted price = Php 30,000 - Php 3,000 = Php 27,000. Next, calculate the 12% VAT on the discounted price: VAT amount = 0.12 * Php 27,000 = Php 3,240. Finally, add the VAT to the discounted price to get the final price: Final price = Php 27,000 + Php 3,240 = Php 30,240.

Pipe A's filling rate is 1/6 of the tank per hour. Pipe B's filling rate is 1/9 of the tank per hour. When both pipes work together, their rates add up. Combined rate = (1/6) + (1/9). To add these fractions, find a common denominator, which is 18. Combined rate = (3/18) + (2/18) = 5/18 of the tank per hour. The time it takes to fill the entire tank (1 whole) is the reciprocal of the combined rate: Time = 1 / (5/18) = 18/5 = 3.6 hours.

Follow the order of operations (PEMDAS/BODMAS). First, calculate the square root: sqrt(144) = 12. Next, calculate the exponent: 3^3 = 3 * 3 * 3 = 27. Next, perform the division: 20 / 4 = 5. Now substitute these values back into the expression: 12 + 27 - 5. Perform addition: 12 + 27 = 39. Perform subtraction: 39 - 5 = 34.

The ratio of red to blue files is 4:7. This means there are 4 + 7 = 11 total parts in the ratio. If 11 parts correspond to 33 files, then one part corresponds to 33 / 11 = 3 files. The number of blue files is represented by 7 parts, so there are 7 * 3 = 21 blue files.

First, determine the official's age 10 years ago: 50 - 10 = 40 years old. Ten years ago, the official was twice as old as his subordinate, so the subordinate's age 10 years ago was 40 / 2 = 20 years old. To find the subordinate's age now, add 10 years to their age from 10 years ago: 20 + 10 = 30 years old.

First, calculate the budget after a 10% increase: Php 500,000 * (1 + 0.10) = Php 500,000 * 1.10 = Php 550,000. Next, calculate the budget after a 10% decrease from the *new* budget (Php 550,000): Php 550,000 * (1 - 0.10) = Php 550,000 * 0.90 = Php 495,000. Note that a 10% increase followed by a 10% decrease does not result in the original amount.

Amount received by Department A = 0.35 * Php 15,000 = Php 5,250. Amount received by Department B = 0.40 * Php 15,000 = Php 6,000. Total received by Departments A and B = Php 5,250 + Php 6,000 = Php 11,250. Amount received by Department C = Total fund - (A + B) = Php 15,000 - Php 11,250 = Php 3,750.

Let the two numbers be x and y, where x is the larger number. We have two equations: 1) x + y = 85 and 2) x - y = 25. Add the two equations together: (x + y) + (x - y) = 85 + 25. This simplifies to 2x = 110. Divide by 2: x = 55. So, the larger number is 55. (If you substitute x=55 into the first equation, 55 + y = 85, so y = 30, which is the smaller number).

Given that 1 cubic meter is equivalent to 1,000 liters. The drum has a capacity of 1,000 liters. Therefore, its capacity in cubic meters is 1,000 liters / 1,000 liters/cubic meter = 1 cubic meter.

This is a permutation problem because the order in which the places are awarded matters (Gold, Silver, Bronze are distinct positions). We are choosing 3 participants out of 8 and arranging them. The formula for permutations P(n, k) = n! / (n-k)!, where n is the total number of items and k is the number of items to choose. P(8, 3) = 8! / (8-3)! = 8! / 5! = 8 * 7 * 6 = 336 ways.

First, sum the percentages allocated for education, health, and infrastructure: 30% + 25% + 20% = 75%. The remaining percentage for administrative expenses is 100% - 75% = 25%. We are given that this 25% amounts to Php 1,500,000. Let 'B' be the total municipal budget. So, 0.25 * B = Php 1,500,000. To find B, divide Php 1,500,000 by 0.25: B = Php 1,500,000 / 0.25 = Php 6,000,000.

Observe the pattern of operations between consecutive numbers: 5 * 2 = 10; 10 - 2 = 8; 8 * 2 = 16; 16 - 2 = 14; 14 * 2 = 28. The pattern is alternating multiplication by 2 and subtraction by 2. The last operation was multiplication by 2, so the next operation should be subtraction by 2. Therefore, 28 - 2 = 26.

Total chairs = 750. First batch delivery: (2/5) * 750 = 300 chairs. Remaining chairs after first batch: 750 - 300 = 450 chairs. Second batch delivery: (1/3) * 450 = 150 chairs. Total chairs delivered: 300 + 150 = 450 chairs. Chairs still to be delivered: 750 - 450 = 300 chairs.

Let original price be P and original quantity be Q. Original budget = P*Q. New price = P * (1 + 0.08) = 1.08P. Let the new quantity be Q'. The budget remains the same, so 1.08P * Q' = P*Q. Q' = (P*Q) / (1.08P) = Q / 1.08. To find the percentage reduction, calculate (Original Q - New Q') / Original Q * 100. Percentage reduction = (Q - Q/1.08) / Q * 100 = (1 - 1/1.08) * 100 = ( (1.08 - 1) / 1.08 ) * 100 = (0.08 / 1.08) * 100. (0.08 / 1.08) is approximately 0.074074. So, 0.074074 * 100 = 7.41%.

Area of the conference room = Length * Width = 12 meters * 9 meters = 108 square meters. Area of one square tile = side * side = 0.5 meters * 0.5 meters = 0.25 square meters. Number of tiles needed = Area of room / Area of one tile = 108 / 0.25. Dividing by 0.25 is equivalent to multiplying by 4. So, 108 * 4 = 432 tiles.

First, find the fraction of the fund contributed by X and Y: 2/7 + 1/3. To add these fractions, find a common denominator, which is 21. (6/21) + (7/21) = 13/21. This means X and Y contributed 13/21 of the total fund. The remaining fraction, contributed by Z, is 1 - 13/21 = 8/21. If 8/21 of the fund is Php 800, then 1/21 of the fund is Php 800 / 8 = Php 100. The total fund (21/21) is 21 * Php 100 = Php 2,100.

First, calculate the total number of pens. 1 dozen = 12 pens, so 12 dozen = 12 * 12 = 144 pens. Next, calculate the total cost by multiplying the number of pens by the cost per pen: 144 pens * Php 8.50/pen = Php 1,224.

Population after 1 year: 2,500 * (1 + 0.04) = 2,500 * 1.04 = 2,600. Population after 2 years: 2,600 * (1 + 0.04) = 2,600 * 1.04 = 2,704. Alternatively, using the compound interest formula: P(1+r)^n = 2500 * (1.04)^2 = 2500 * 1.0816 = 2,704.

Initial amount of alcohol = 25% of 40 liters = 0.25 * 40 = 10 liters. When 10 liters of pure alcohol are added: New total amount of alcohol = 10 liters (initial) + 10 liters (added) = 20 liters. New total volume of solution = 40 liters (initial) + 10 liters (added) = 50 liters. New percentage of alcohol = (New total alcohol / New total solution) * 100 = (20 / 50) * 100 = (2/5) * 100 = 40%.

To add and subtract fractions, find a common denominator. The least common multiple of 4, 2, and 8 is 8. Convert the fractions: (3/4) = (6/8), (1/2) = (4/8). Now perform the operations: (6/8) + (4/8) - (1/8) = (6 + 4 - 1) / 8 = 9/8.

To find the maximum number of adults, divide the maximum load capacity by the average weight of one adult. Maximum number of adults = 600 kg / 75 kg/adult = 8 adults.

Let the principal be P. If it doubles, the total amount A = 2P. Simple Interest (I) = A - P = 2P - P = P. The formula for simple interest is I = P * R * T. So, P = P * R * 5. Divide both sides by P: 1 = R * 5. Solve for R: R = 1/5 = 0.20. As a percentage, the annual rate of interest is 0.20 * 100% = 20%.

First, calculate the total number of sheets used in 4 weeks: 2,500 sheets/week * 4 weeks = 10,000 sheets. Next, determine how many reams this quantity represents. Since 1 ream = 500 sheets, number of reams = 10,000 sheets / 500 sheets/ream = 20 reams.

To find the smallest positive integer divisible by 3, 4, and 5, we need to find their Least Common Multiple (LCM). Since 3, 4, and 5 are pairwise coprime (they share no common factors other than 1), their LCM is simply their product. LCM(3, 4, 5) = 3 * 4 * 5 = 60.

The base fare for the first 4 kilometers is Php 13.00. The total ride is 10 kilometers, so the succeeding kilometers are 10 - 4 = 6 kilometers. The cost for the succeeding kilometers is 6 km * Php 2.50/km = Php 15.00. Total fare = Base fare + Succeeding kilometers cost = Php 13.00 + Php 15.00 = Php 28.00.

First, calculate the hourly rate: Php 650 / 8 hours = Php 81.25 per hour. Then, calculate the earnings for 12 hours: Php 81.25/hour * 12 hours = Php 975.

First, calculate the total percentage allocated for construction and equipment: 40% + 30% = 70%. The remaining percentage is 100% - 70% = 30%. The amount remaining for administrative tasks is 30% of Php 1,500,000 = 0.30 * Php 1,500,000 = Php 450,000. This amount is divided equally between two administrative tasks, so each task receives Php 450,000 / 2 = Php 225,000.

Follow the order of operations. First, perform the multiplication: 0.25 * 12 = 3. Next, calculate '1/3 of 60': (1/3) * 60 = 20. Next, calculate the square root: sqrt(49) = 7. Now substitute these values back into the expression: 3 + 20 - 7. Perform addition: 3 + 20 = 23. Perform subtraction: 23 - 7 = 16.

Total vehicles = 12. Number of sedans = (1/4) * 12 = 3 sedans. Number of vans = (1/3) * 12 = 4 vans. Total sedans and vans = 3 + 4 = 7 vehicles. Number of SUVs = Total vehicles - (Sedans + Vans) = 12 - 7 = 5 SUVs.

The scale 1:50,000 means that 1 cm on the map represents 50,000 cm in actual distance. The distance on the map is 8 cm. So, the actual distance = 8 cm * 50,000 = 400,000 cm. To convert centimeters to kilometers: 1 meter = 100 cm, so 1 km = 1,000 meters = 1,000 * 100 cm = 100,000 cm. Actual distance in km = 400,000 cm / 100,000 cm/km = 4 km.

First, calculate the number of contractual employees: 30% of 450 = 0.30 * 450 = 135 employees. Next, calculate the number of permanent employees: 40% of 450 = 0.40 * 450 = 180 employees. The total percentage of contractual and permanent employees is 30% + 40% = 70%. Therefore, the percentage of probationary employees is 100% - 70% = 30%. The number of probationary employees is 30% of 450 = 0.30 * 450 = 135 employees.

The ratio of successful to unsuccessful examinees is 3:5. This means for every 3 successful examinees, there are 5 unsuccessful ones. The total parts in the ratio are 3 + 5 = 8 parts. If 8 parts represent 2,400 individuals, then one part represents 2,400 / 8 = 300 individuals. The number of successful examinees is represented by 3 parts, so 3 * 300 = 900 successful examinees.

To find the average, sum all the values and divide by the number of values. Sum = 38 + 45 + 52 + 30 + 40 = 205. Number of days = 5. Average = 205 / 5 = 41 documents per day.

First, find the rate per encoder per hour. The total work done is 1,200 records by 5 encoders in 8 hours, which is 5 * 8 = 40 'encoder-hours'. So, the rate is 1,200 records / 40 encoder-hours = 30 records per encoder per hour. Now, for 3 data encoders working for 4 hours, the total 'encoder-hours' is 3 * 4 = 12 encoder-hours. The total records they can input is 12 encoder-hours * 30 records/encoder-hour = 360 records.

Cost for materials = (1/3) * Php 72,000 = Php 24,000. Cost for labor = (1/4) * Php 72,000 = Php 18,000. Total spent on materials and labor = Php 24,000 + Php 18,000 = Php 42,000. The remaining amount for administrative costs = Total budget - (Materials + Labor) = Php 72,000 - Php 42,000 = Php 30,000.

First, find the absolute increase: 300 - 250 = 50 applicants. To find the percentage increase, divide the increase by the original number of applicants and multiply by 100. Percentage increase = (50 / 250) * 100 = (1/5) * 100 = 20%.

To fence the property, you need to find its perimeter. The perimeter of a rectangle is 2 * (length + width). Perimeter = 2 * (60 m + 45 m) = 2 * 105 m = 210 meters. The total cost of fencing is the perimeter multiplied by the cost per meter. Total cost = 210 meters * Php 150/meter = Php 31,500.

The formula for time is Distance / Speed. Time = 360 km / 80 km/h = 4.5 hours.

First, apply the 10% discount: Discount amount = 0.10 * Php 25,000 = Php 2,500. Price after first discount = Php 25,000 - Php 2,500 = Php 22,500. Next, apply the additional 5% discount to the new price: Second discount amount = 0.05 * Php 22,500 = Php 1,125. Final price = Php 22,500 - Php 1,125 = Php 21,375.

Simple Interest (I) = Principal (P) * Rate (R) * Time (T). I = Php 50,000 * 0.06 * 3 = Php 9,000. The total amount to pay back is the Principal + Simple Interest. Total amount = Php 50,000 + Php 9,000 = Php 59,000.

First, convert 2 hours to minutes: 2 hours * 60 minutes/hour = 120 minutes. Next, find the printing rate per minute: 2,400 pages / 30 minutes = 80 pages/minute. Finally, calculate the total pages printed in 120 minutes: 80 pages/minute * 120 minutes = 9,600 pages.

This is a weighted average problem. Multiply each score by its corresponding percentage (as a decimal) and sum the results. Average score = (0.60 * 4) + (0.30 * 3) + (0.10 * 1) = 2.4 + 0.9 + 0.1 = 3.4.

Let the age of the younger colleague be 'x'. Then the age of the older colleague is 'x + 8'. The sum of their ages is 72, so x + (x + 8) = 72. This simplifies to 2x + 8 = 72. Subtract 8 from both sides: 2x = 64. Divide by 2: x = 32. So, the younger colleague is 32 years old.

First, calculate the total volume (capacity) of the tank. Volume of a rectangular prism = Length * Width * Height = 5 m * 3 m * 2 m = 30 cubic meters. The tank is filled to 3/4 of its capacity, so the volume of water is (3/4) * 30 cubic meters = 22.5 cubic meters.

Observe the differences between consecutive numbers: 11 - 7 = 4, 16 - 11 = 5, 22 - 16 = 6, 29 - 22 = 7. The differences are increasing by 1 each time (4, 5, 6, 7). Therefore, the next difference should be 8. So, the next number in the sequence is 29 + 8 = 37.

Total cost of rice = Php 4,800. Revenue from the first batch: 100 kg * Php 35/kg = Php 3,500. Revenue from the remaining batch: 50 kg * Php 30/kg = Php 1,500. Total revenue = Php 3,500 + Php 1,500 = Php 5,000. Profit/Loss = Total Revenue - Total Cost = Php 5,000 - Php 4,800 = Php 200. Since the result is positive, it's a profit.

Let M be the number of motorcycles and C be the number of cars. We have two equations: 1) M + C = 65 (total vehicles), 2) 2M + 4C = 210 (total wheels). From equation 1, M = 65 - C. Substitute this into equation 2: 2(65 - C) + 4C = 210. Simplify: 130 - 2C + 4C = 210. Combine like terms: 130 + 2C = 210. Subtract 130 from both sides: 2C = 80. Divide by 2: C = 40. So, there are 40 cars.

First, calculate the total percentage of deductions: 15% (taxes) + 5% (health insurance) = 20%. Next, calculate the total deduction amount: 20% of Php 32,500 = 0.20 * Php 32,500 = Php 6,500. Finally, subtract the total deductions from the gross salary to find the net salary: Php 32,500 - Php 6,500 = Php 26,000.

The total number of ratio parts is 2 + 3 + 4 = 9 parts. The value of one part is the total bonus divided by the total parts: Php 18,000 / 9 = Php 2,000. Employee B receives 3 parts, so Employee B will receive 3 * Php 2,000 = Php 6,000.

For a square, the perimeter is 4 times the length of one side (P = 4s). Given the perimeter is 48 meters, the side length (s) = 48 meters / 4 = 12 meters. The area of a square is side * side (A = s^2). Area = 12 meters * 12 meters = 144 square meters.

Let 'D' be the number of dengue cases in December. January's cases were 20% more than December's, which means January's cases are 100% + 20% = 120% of December's cases. So, 1.20 * D = 120. To find D, divide 120 by 1.20: D = 120 / 1.20 = 100 cases. Therefore, 100 dengue cases were recorded in December.

First, calculate the funding for infrastructure development: (5/8) * Php 1,200,000 = Php 750,000. Next, find the remaining funds: Php 1,200,000 - Php 750,000 = Php 450,000. Finally, calculate the allocation for personnel salaries, which is 1/3 of the remaining funds: (1/3) * Php 450,000 = Php 150,000.

Employee A's rate is 1/10 of the task per hour. Employee B's rate is 1/15 of the task per hour. When they work together, their rates add up: (1/10) + (1/15) = (3/30) + (2/30) = 5/30 = 1/6 of the task per hour. If they complete 1/6 of the task per hour, they will complete the entire task (1 whole task) in 1 / (1/6) = 6 hours.

To find when they will next be at the terminal together, we need to find the Least Common Multiple (LCM) of their return intervals (45 minutes and 60 minutes). Prime factorization of 45 = 3^2 * 5. Prime factorization of 60 = 2^2 * 3 * 5. LCM(45, 60) = 2^2 * 3^2 * 5 = 4 * 9 * 5 = 180 minutes. 180 minutes is equal to 3 hours. Since they both left at 6:00 AM, they will next be at the terminal together 3 hours later, which is 9:00 AM.

First, calculate the total number of pens in the bag: 8 (red) + 5 (blue) + 7 (black) = 20 pens. The number of blue pens is 5. Probability is calculated as (Number of favorable outcomes) / (Total number of possible outcomes). So, the probability of drawing a blue pen is 5/20, which simplifies to 1/4.

Let 'S' be the original monthly salary. A 15% increase means the new salary is 100% + 15% = 115% of the original salary. So, 1.15 * S = Php 28,750. To find S, divide the new salary by 1.15: S = Php 28,750 / 1.15 = Php 25,000.

To find the amount of pure acid, multiply the total volume of the solution by the percentage of acid. Amount of pure acid = 30% of 20 liters = 0.30 * 20 = 6 liters.

This is a geometric progression where each term is obtained by multiplying the previous term by 3. 3 * 3 = 9, 9 * 3 = 27. So, the missing number is 27 * 3 = 81. To verify, 81 * 3 = 243.

First, convert all proportions to fractions or decimals. 0.4 as a fraction is 4/10, which simplifies to 2/5. So, fiction books are 2/5 of the total. Reference books are 1/5 of the total. Total fraction of fiction and reference books = 2/5 + 1/5 = 3/5. The remaining books are non-fiction, so 1 (whole) - 3/5 = 2/5 of the books are non-fiction.

Number of days remaining in March (March has 31 days): 31 - 15 = 16 days. Remaining days for the project: 75 - 16 = 59 days. April has 30 days. Subtract April's days from the remaining: 59 - 30 = 29 days. These 29 days will fall in May. So, the project is expected to be completed on May 29, 2023.

Let the number of male employees be 7x and female employees be 5x. The difference in their numbers is 7x - 5x = 2x. We are given that this difference is 24, so 2x = 24. Dividing by 2, we get x = 12. Number of male employees = 7 * 12 = 84. Number of female employees = 5 * 12 = 60. Total number of employees = 84 + 60 = 144.

Follow the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). First, Exponents: 5^2 = 25. Next, Division: 18 / 3 = 6. Next, Multiplication: 2 * 4 = 8. Now substitute these values back into the expression: 25 + 6 - 8. Perform Addition: 25 + 6 = 31. Perform Subtraction: 31 - 8 = 23.

This is a percentage of a percentage calculation. We need to find 25% of the 60% of employees. Convert percentages to decimals: 0.25 * 0.60 = 0.15. Convert back to percentage: 0.15 * 100% = 15%. So, 15% of the total employees expressed interest in additional health programs.

To find the median, first arrange the bids in ascending order: Php 110,000, Php 115,000, Php 120,000, Php 125,000, Php 130,000, Php 135,000, Php 140,000. Since there are 7 bids (an odd number), the median is the middle value. In a set of 7 values, the 4th value is the median. The 4th value in the ordered list is Php 125,000.

Supplementary angles are two angles whose sum is 180 degrees. If one angle measures 75 degrees, then the other angle measures 180 degrees - 75 degrees = 105 degrees.

By 9:00 AM, the first courier has traveled for 1 hour (from 8:00 AM to 9:00 AM) at a speed of 50 km/h. So, the first courier is 50 km away from the office. The second courier starts at 9:00 AM. The relative speed at which the second courier closes the gap on the first courier is the difference in their speeds: 75 km/h - 50 km/h = 25 km/h. The time it will take for the second courier to cover the 50 km lead of the first courier is Distance / Relative Speed = 50 km / 25 km/h = 2 hours. Since the second courier started at 9:00 AM, they will overtake the first courier 2 hours later, which is 11:00 AM.

The area of a circle is given by the formula A = pi * r^2, where r is the radius. Given radius r = 7 meters and pi = 22/7. Area = (22/7) * (7 meters)^2 = (22/7) * 49 square meters. Area = 22 * (49/7) square meters = 22 * 7 square meters = 154 square meters.

Let the smallest even integer be 'x'. Since they are consecutive even integers, the next two would be 'x + 2' and 'x + 4'. Their sum is 108: x + (x + 2) + (x + 4) = 108. Combine like terms: 3x + 6 = 108. Subtract 6 from both sides: 3x = 102. Divide by 3: x = 34. The smallest integer is 34. (The integers are 34, 36, 38).

First, calculate the price after the 10% discount: Discount amount = 0.10 * Php 30,000 = Php 3,000. Discounted price = Php 30,000 - Php 3,000 = Php 27,000. Next, calculate the 12% VAT on the discounted price: VAT amount = 0.12 * Php 27,000 = Php 3,240. Finally, add the VAT to the discounted price to get the final price: Final price = Php 27,000 + Php 3,240 = Php 30,240.

Pipe A's filling rate is 1/6 of the tank per hour. Pipe B's filling rate is 1/9 of the tank per hour. When both pipes work together, their rates add up. Combined rate = (1/6) + (1/9). To add these fractions, find a common denominator, which is 18. Combined rate = (3/18) + (2/18) = 5/18 of the tank per hour. The time it takes to fill the entire tank (1 whole) is the reciprocal of the combined rate: Time = 1 / (5/18) = 18/5 = 3.6 hours.

Follow the order of operations (PEMDAS/BODMAS). First, calculate the square root: sqrt(144) = 12. Next, calculate the exponent: 3^3 = 3 * 3 * 3 = 27. Next, perform the division: 20 / 4 = 5. Now substitute these values back into the expression: 12 + 27 - 5. Perform addition: 12 + 27 = 39. Perform subtraction: 39 - 5 = 34.

The ratio of red to blue files is 4:7. This means there are 4 + 7 = 11 total parts in the ratio. If 11 parts correspond to 33 files, then one part corresponds to 33 / 11 = 3 files. The number of blue files is represented by 7 parts, so there are 7 * 3 = 21 blue files.

First, determine the official's age 10 years ago: 50 - 10 = 40 years old. Ten years ago, the official was twice as old as his subordinate, so the subordinate's age 10 years ago was 40 / 2 = 20 years old. To find the subordinate's age now, add 10 years to their age from 10 years ago: 20 + 10 = 30 years old.

First, calculate the budget after a 10% increase: Php 500,000 * (1 + 0.10) = Php 500,000 * 1.10 = Php 550,000. Next, calculate the budget after a 10% decrease from the *new* budget (Php 550,000): Php 550,000 * (1 - 0.10) = Php 550,000 * 0.90 = Php 495,000. Note that a 10% increase followed by a 10% decrease does not result in the original amount.

Amount received by Department A = 0.35 * Php 15,000 = Php 5,250. Amount received by Department B = 0.40 * Php 15,000 = Php 6,000. Total received by Departments A and B = Php 5,250 + Php 6,000 = Php 11,250. Amount received by Department C = Total fund - (A + B) = Php 15,000 - Php 11,250 = Php 3,750.

Let the two numbers be x and y, where x is the larger number. We have two equations: 1) x + y = 85 and 2) x - y = 25. Add the two equations together: (x + y) + (x - y) = 85 + 25. This simplifies to 2x = 110. Divide by 2: x = 55. So, the larger number is 55. (If you substitute x=55 into the first equation, 55 + y = 85, so y = 30, which is the smaller number).

Given that 1 cubic meter is equivalent to 1,000 liters. The drum has a capacity of 1,000 liters. Therefore, its capacity in cubic meters is 1,000 liters / 1,000 liters/cubic meter = 1 cubic meter.

This is a permutation problem because the order in which the places are awarded matters (Gold, Silver, Bronze are distinct positions). We are choosing 3 participants out of 8 and arranging them. The formula for permutations P(n, k) = n! / (n-k)!, where n is the total number of items and k is the number of items to choose. P(8, 3) = 8! / (8-3)! = 8! / 5! = 8 * 7 * 6 = 336 ways.

First, sum the percentages allocated for education, health, and infrastructure: 30% + 25% + 20% = 75%. The remaining percentage for administrative expenses is 100% - 75% = 25%. We are given that this 25% amounts to Php 1,500,000. Let 'B' be the total municipal budget. So, 0.25 * B = Php 1,500,000. To find B, divide Php 1,500,000 by 0.25: B = Php 1,500,000 / 0.25 = Php 6,000,000.

Observe the pattern of operations between consecutive numbers: 5 * 2 = 10; 10 - 2 = 8; 8 * 2 = 16; 16 - 2 = 14; 14 * 2 = 28. The pattern is alternating multiplication by 2 and subtraction by 2. The last operation was multiplication by 2, so the next operation should be subtraction by 2. Therefore, 28 - 2 = 26.

Total chairs = 750. First batch delivery: (2/5) * 750 = 300 chairs. Remaining chairs after first batch: 750 - 300 = 450 chairs. Second batch delivery: (1/3) * 450 = 150 chairs. Total chairs delivered: 300 + 150 = 450 chairs. Chairs still to be delivered: 750 - 450 = 300 chairs.

Let original price be P and original quantity be Q. Original budget = P*Q. New price = P * (1 + 0.08) = 1.08P. Let the new quantity be Q'. The budget remains the same, so 1.08P * Q' = P*Q. Q' = (P*Q) / (1.08P) = Q / 1.08. To find the percentage reduction, calculate (Original Q - New Q') / Original Q * 100. Percentage reduction = (Q - Q/1.08) / Q * 100 = (1 - 1/1.08) * 100 = ( (1.08 - 1) / 1.08 ) * 100 = (0.08 / 1.08) * 100. (0.08 / 1.08) is approximately 0.074074. So, 0.074074 * 100 = 7.41%.

Area of the conference room = Length * Width = 12 meters * 9 meters = 108 square meters. Area of one square tile = side * side = 0.5 meters * 0.5 meters = 0.25 square meters. Number of tiles needed = Area of room / Area of one tile = 108 / 0.25. Dividing by 0.25 is equivalent to multiplying by 4. So, 108 * 4 = 432 tiles.

First, find the fraction of the fund contributed by X and Y: 2/7 + 1/3. To add these fractions, find a common denominator, which is 21. (6/21) + (7/21) = 13/21. This means X and Y contributed 13/21 of the total fund. The remaining fraction, contributed by Z, is 1 - 13/21 = 8/21. If 8/21 of the fund is Php 800, then 1/21 of the fund is Php 800 / 8 = Php 100. The total fund (21/21) is 21 * Php 100 = Php 2,100.

First, calculate the total number of pens. 1 dozen = 12 pens, so 12 dozen = 12 * 12 = 144 pens. Next, calculate the total cost by multiplying the number of pens by the cost per pen: 144 pens * Php 8.50/pen = Php 1,224.

Population after 1 year: 2,500 * (1 + 0.04) = 2,500 * 1.04 = 2,600. Population after 2 years: 2,600 * (1 + 0.04) = 2,600 * 1.04 = 2,704. Alternatively, using the compound interest formula: P(1+r)^n = 2500 * (1.04)^2 = 2500 * 1.0816 = 2,704.

Initial amount of alcohol = 25% of 40 liters = 0.25 * 40 = 10 liters. When 10 liters of pure alcohol are added: New total amount of alcohol = 10 liters (initial) + 10 liters (added) = 20 liters. New total volume of solution = 40 liters (initial) + 10 liters (added) = 50 liters. New percentage of alcohol = (New total alcohol / New total solution) * 100 = (20 / 50) * 100 = (2/5) * 100 = 40%.

To add and subtract fractions, find a common denominator. The least common multiple of 4, 2, and 8 is 8. Convert the fractions: (3/4) = (6/8), (1/2) = (4/8). Now perform the operations: (6/8) + (4/8) - (1/8) = (6 + 4 - 1) / 8 = 9/8.

To find the maximum number of adults, divide the maximum load capacity by the average weight of one adult. Maximum number of adults = 600 kg / 75 kg/adult = 8 adults.

Let the principal be P. If it doubles, the total amount A = 2P. Simple Interest (I) = A - P = 2P - P = P. The formula for simple interest is I = P * R * T. So, P = P * R * 5. Divide both sides by P: 1 = R * 5. Solve for R: R = 1/5 = 0.20. As a percentage, the annual rate of interest is 0.20 * 100% = 20%.

First, calculate the total number of sheets used in 4 weeks: 2,500 sheets/week * 4 weeks = 10,000 sheets. Next, determine how many reams this quantity represents. Since 1 ream = 500 sheets, number of reams = 10,000 sheets / 500 sheets/ream = 20 reams.

To find the smallest positive integer divisible by 3, 4, and 5, we need to find their Least Common Multiple (LCM). Since 3, 4, and 5 are pairwise coprime (they share no common factors other than 1), their LCM is simply their product. LCM(3, 4, 5) = 3 * 4 * 5 = 60.

The base fare for the first 4 kilometers is Php 13.00. The total ride is 10 kilometers, so the succeeding kilometers are 10 - 4 = 6 kilometers. The cost for the succeeding kilometers is 6 km * Php 2.50/km = Php 15.00. Total fare = Base fare + Succeeding kilometers cost = Php 13.00 + Php 15.00 = Php 28.00.

First, calculate the hourly rate: Php 650 / 8 hours = Php 81.25 per hour. Then, calculate the earnings for 12 hours: Php 81.25/hour * 12 hours = Php 975.

First, calculate the total percentage allocated for construction and equipment: 40% + 30% = 70%. The remaining percentage is 100% - 70% = 30%. The amount remaining for administrative tasks is 30% of Php 1,500,000 = 0.30 * Php 1,500,000 = Php 450,000. This amount is divided equally between two administrative tasks, so each task receives Php 450,000 / 2 = Php 225,000.

Follow the order of operations. First, perform the multiplication: 0.25 * 12 = 3. Next, calculate '1/3 of 60': (1/3) * 60 = 20. Next, calculate the square root: sqrt(49) = 7. Now substitute these values back into the expression: 3 + 20 - 7. Perform addition: 3 + 20 = 23. Perform subtraction: 23 - 7 = 16.

Total vehicles = 12. Number of sedans = (1/4) * 12 = 3 sedans. Number of vans = (1/3) * 12 = 4 vans. Total sedans and vans = 3 + 4 = 7 vehicles. Number of SUVs = Total vehicles - (Sedans + Vans) = 12 - 7 = 5 SUVs.

The scale 1:50,000 means that 1 cm on the map represents 50,000 cm in actual distance. The distance on the map is 8 cm. So, the actual distance = 8 cm * 50,000 = 400,000 cm. To convert centimeters to kilometers: 1 meter = 100 cm, so 1 km = 1,000 meters = 1,000 * 100 cm = 100,000 cm. Actual distance in km = 400,000 cm / 100,000 cm/km = 4 km.