Three numbers are in the ratio 3:5:7. If the sum of the first and third is 300 and the sum of all three is 450, what is the second number?
Explanation: Let the numbers be 3x, 5x, 7x. Sum = 15x = 450, so x = 30. The numbers are 90, 150, 210. The second number is 150. Check: first + third = 90+210 = 300.
Four numbers are in the ratio 1:2:3:5. If their product is 480, what is the sum of the first and fourth numbers?
Explanation: Let numbers be 1k, 2k, 3k, 5k. Product = 30k⁴ = 480, so k⁴ = 16, k = 2. Numbers: 2, 4, 6, 10. Sum of first and fourth = 2+10 = 12.
₹5,000 is to be divided among A, B, and C. A gets 2/5 of the total. The remainder is divided between B and C in the ratio 3:2. How much more does B get than C?
Explanation: A gets 2/5 of ₹5000 = ₹2000. Remainder = ₹3000. B gets 3/5 × ₹3000 = ₹1800. C gets 2/5 × ₹3000 = ₹1200. Difference B-C = ₹1800 - ₹1200 = ₹600.
The incomes of A and B are in the ratio 3:4. If A's income increases by 20% and B's income decreases by 15%, what is the new ratio of their incomes?
Explanation: New income of A = 3 × 1.20 = 3.6. New income of B = 4 × 0.85 = 3.4. Ratio = 3.6:3.4 = 36:34 = 18:17.
Two alloys of copper and zinc are mixed. Alloy X has Cu and Zn in ratio 3:2. Alloy Y has Cu and Zn in ratio 5:3. They are mixed in the ratio 2:3 by weight. What is the ratio of copper to zinc in the new alloy?
Explanation: In 2 units of X: Cu = 2×(3/5) = 6/5, Zn = 2×(2/5) = 4/5. In 3 units of Y: Cu = 3×(5/8) = 15/8, Zn = 3×(3/8) = 9/8. Total Cu = 6/5 + 15/8 = 123/40. Total Zn = 4/5 + 9/8 = 77/40. Ratio = 123:77.
Three vessels contain mixtures of milk and water. Vessel A (10L) has milk and water in ratio 2:3. Vessel B (12L) has ratio 3:1. Vessel C (15L) has ratio 1:4. If all three are poured into a large container, what is the ratio of milk to water?
Explanation: Vessel A: Milk = 10×(2/5) = 4L, Water = 6L. Vessel B: Milk = 12×(3/4) = 9L, Water = 3L. Vessel C: Milk = 15×(1/5) = 3L, Water = 12L. Total milk = 16L, Total water = 21L. Ratio = 16:21.
The incomes of A and B are in the ratio 3:2. Their expenditures are in the ratio 5:3. If both save ₹1,000, what is the income of A?
- ₹6,000
- ₹5,000
- ₹3,000
- ₹4,000
Explanation: Let incomes be 3x and 2x, expenditures be 5y and 3y. Both save ₹1000: 3x-5y = 1000 and 2x-3y = 1000. Subtracting: x = 2y. Substituting: 3(2y)-5y = y = 1000. So x = 2000. A's income = 3×2000 = ₹6000.
The present ages of A and B are in the ratio 5:3. Four years ago, their ages were in the ratio 2:1. What is the sum of their present ages?
- 24 years
- 36 years
- 32 years
- 28 years
Explanation: Let present ages be 5x and 3x. Four years ago: (5x-4)/(3x-4) = 2/1. Cross-multiply: 5x-4 = 6x-8, so x = 4. Present ages: 20 and 12. Sum = 32 years.
The three angles of a triangle are in arithmetic progression. The ratio of the smallest angle to the largest angle is 1:3. What is the measure of the largest angle?
Explanation: Let angles be (a-d), a, (a+d). Sum = 3a = 180°, so a = 60°. Given (a-d)/(a+d) = 1/3: 3(60-d) = 60+d, 180-3d = 60+d, 4d = 120, d = 30°. Angles: 30°, 60°, 90°. Largest = 90°.
A container has 20 litres of a mixture of milk and water in the ratio 7:3. If 5 litres of the mixture is removed and replaced with pure water, what is the new ratio of milk to water?
Explanation: Original: Milk = 20×(7/10) = 14L, Water = 6L. In 5L removed: Milk = 5×(7/10) = 3.5L, Water = 1.5L. Remaining: Milk = 10.5L, Water = 4.5L. After adding 5L water: Milk = 10.5L, Water = 9.5L. Ratio = 10.5:9.5 = 21:19.
A and B travel the same distance. The ratio of their speeds is 3:4. If A takes 2 hours more than B to complete the journey, how long does B take?
- 3 hours
- 4.5 hours
- 6 hours
- 8 hours
Explanation: Speed ratio 3:4 means time ratio is inverse: 4:3. Let times be 4x and 3x. Difference = x = 2 hours. So B takes 3x = 6 hours, A takes 8 hours.
A bag contains ₹1, ₹2, and ₹5 coins in the ratio of 4:3:2. If the total value of the coins is ₹180, how many ₹2 coins are there?
Explanation: Let numbers be 4x, 3x, 2x. Total value = 1(4x) + 2(3x) + 5(2x) = 4x + 6x + 10x = 20x = 180. So x = 9. Number of ₹2 coins = 3×9 = 27.
If 15 workers can complete a piece of work in 24 days, how many days will 18 workers take to complete the same work, assuming all work at the same rate?
- 22 days
- 28 days
- 20 days
- 21 days
Explanation: Workers and days are inversely proportional. 15×24 = 18×d, so d = 360/18 = 20 days.
Pipe A can fill a tank in 12 hours and Pipe B can fill the same tank in 18 hours. If both pipes are opened simultaneously, how long will they take to fill the tank?
- 7 hours 12 minutes
- 15 hours
- 6 hours
- 30 hours
Explanation: Pipe A's rate = 1/12 per hour. Pipe B's rate = 1/18 per hour. Combined rate = 1/12 + 1/18 = 5/36 per hour. Time = 36/5 = 7.2 hours = 7 hours 12 minutes.
8 men working 5 hours a day for 12 days can complete a certain work. How many days will 10 men take to complete the same work if they work 6 hours a day?
- 9 days
- 10 days
- 8 days
- 12 days
Explanation: Total work = 8 men × 5 hours/day × 12 days = 480 man-hours. With 10 men working 6 hours/day: days needed = 480/(10×6) = 8 days.
In a hostel, food is available for 200 students for 30 days. After 10 days, 50 more students join. For how many more days will the remaining food last?
- 12 days
- 24 days
- 20 days
- 16 days
Explanation: Total food = 200×30 = 6000 student-days. After 10 days: 200×10 = 2000 used. Remaining = 4000. With 250 students: 4000/250 = 16 days.
A car covers 420 km in 7 hours. If its speed is increased by 1/3, how long will it take to cover 600 km at the new speed?
- 6 hours
- 10 hours
- 8 hours
- 7.5 hours
Explanation: Original speed = 420/7 = 60 km/h. New speed = 60 + (1/3)×60 = 80 km/h. Time for 600 km = 600/80 = 7.5 hours.
On a map with scale 1:50,000, the distance between two cities is 8 cm. What is the actual distance between the cities?
Explanation: Actual distance = 8 cm × 50,000 = 400,000 cm = 4,000 m = 4 km.
12 men earn ₹900 in 5 days. How many days will 8 men take to earn ₹1,200?
- 12 days
- 10 days
- 15 days
- 8 days
Explanation: Rate per man per day = ₹900/(12×5) = ₹15. For 8 men to earn ₹1200: days = 1200/(8×15) = 10 days.
6 machines running for 3 hours produce 270 bottles. How many bottles will 8 machines produce in 5 hours?
Explanation: Rate per machine per hour = 270/(6×3) = 15 bottles. With 8 machines for 5 hours: 8×5×15 = 600 bottles.
If 5 kg of rice costs ₹120, what is the cost of 8 kg of rice at the same rate?
Explanation: Cost per kg = ₹120/5 = ₹24. Cost of 8 kg = 24×8 = ₹192.
A 6-metre tall pole casts a shadow of 4 metres. At the same time, what will be the length of the shadow cast by a 15-metre tall building?
- 22.5 metres
- 10 metres
- 8 metres
- 12 metres
Explanation: Height and shadow length are directly proportional. 6/4 = 15/x, so x = (15×4)/6 = 10 metres.
A can complete a work in 8 days and B can complete the same work in 12 days. They work together and earn ₹4,000. What is A's share?
- ₹1,600
- ₹2,400
- ₹3,200
- ₹2,000
Explanation: Work ratio A:B = 1/8 : 1/12 = 3:2. A's share = (3/5)×4000 = ₹2,400. B's share = (2/5)×4000 = ₹1,600.
A pump can fill a tank in 8 hours. Due to a leak, it takes 12 hours to empty the full tank. If the tank is empty and the pump is started, how long will it take to fill the tank?
- 20 hours
- 4 hours
- 24 hours
- 48 hours
Explanation: Pump rate = 1/8 per hour. Leak rate = 1/12 per hour. Net rate = 1/8 - 1/12 = 1/24 per hour. Time to fill = 24 hours.
A, B, and C start a business by investing ₹5,000, ₹8,000, and ₹7,000 respectively. If the total profit at the end of the year is ₹6,000, what is B's share of the profit?
- ₹2,100
- ₹3,000
- ₹1,500
- ₹2,400
Explanation: Investment ratio = 5000:8000:7000 = 5:8:7. Total parts = 20. B's share = (8/20)×6000 = ₹2,400.
A invests ₹12,000 for 12 months, B invests ₹15,000 for 8 months, and C invests ₹10,000 for 6 months in a business. If the profit is ₹13,500, what is A's share?
- ₹5,000
- ₹4,500
- ₹2,500
- ₹6,000
Explanation: Equivalent capital ratio = (12000×12):(15000×8):(10000×6) = 144000:120000:60000 = 12:10:5. Total parts = 27. A's share = (12/27)×13500 = ₹6,000.
A invests ₹5,000 for the entire year. B invests ₹6,000 for the first 6 months and then withdraws ₹2,000, leaving ₹4,000 invested for the next 6 months. If the profit is ₹3,300, what is A's share?
- ₹1,800
- ₹1,650
- ₹1,500
- ₹1,980
Explanation: A's equivalent = 5000×12 = 60,000. B's equivalent = 6000×6 + 4000×6 = 36,000 + 24,000 = 60,000. Ratio = 1:1. A's share = 3300/2 = ₹1,650.
A starts a business with ₹8,000. After 4 months, B joins with ₹12,000. After 6 more months, C joins with ₹15,000. At the end of the year, the profit is ₹18,500. What is C's share?
- ₹1,500
- ₹3,000
- ₹2,500
- ₹8,000
Explanation: A's equivalent = 8000×12 = 96,000. B's equivalent = 12000×8 = 96,000. C's equivalent = 15000×2 = 30,000. Ratio = 96:96:30 = 16:16:5. Total = 37. C's share = (5/37)×18500 = ₹2,500.
A and B enter into partnership. A invests ₹15,000 and manages the business. B invests ₹25,000 as a sleeping partner. A receives 10% of the profit for management, and the remaining profit is divided in the ratio of their capitals. If the profit is ₹19,200, what is A's total share?
- ₹9,600
- ₹8,400
- ₹10,800
- ₹7,200
Explanation: Management fee = 10% of 19200 = ₹1,920. Remaining = ₹17,280. Capital ratio = 15000:25000 = 3:5. A's capital share = (3/8)×17280 = ₹6,480. A's total = 1920 + 6480 = ₹8,400.
A invests ₹4,000 for the first 3 months and then increases his investment to ₹7,000 for the remaining 9 months. B invests ₹5,000 for the first 6 months and then reduces to ₹3,000 for the next 6 months. If the profit is ₹12,300, what is A's share?
- ₹6,000
- ₹4,800
- ₹8,000
- ₹7,500
Explanation: A's equivalent = 4000×3 + 7000×9 = 12,000 + 63,000 = 75,000. B's equivalent = 5000×6 + 3000×6 = 30,000 + 18,000 = 48,000. Ratio = 75:48 = 25:16. Total = 41. A's share = (25/41)×12300 = ₹7,500.
A and B start a business with capitals of ₹20,000 and ₹30,000 respectively. They agree to pay 5% interest on capital and divide the remaining profit in the ratio 2:3 for their work contribution. If the profit is ₹18,000, what is A's total share?
- ₹6,200
- ₹7,800
- ₹8,000
- ₹7,200
Explanation: Interest on capital: A = 5% of 20000 = ₹1,000. B = 5% of 30000 = ₹1,500. Total interest = ₹2,500. Remaining profit = 18000 - 2500 = ₹15,500. A's work share = (2/5)×15500 = ₹6,200. A's total = 1000 + 6200 = ₹7,200.
A and B start a business. A invests ₹10,000 and B invests ₹15,000. A is the working partner and receives a salary of ₹1,000 per month. The remaining profit is divided in the ratio of their capitals. If the annual profit is ₹42,000, what is A's total share?
- ₹30,000
- ₹24,000
- ₹18,000
- ₹12,000
Explanation: A's annual salary = 1000×12 = ₹12,000. Remaining profit = 42000 - 12000 = ₹30,000. Capital ratio = 10000:15000 = 2:3. A's profit share = (2/5)×30000 = ₹12,000. A's total = 12000 + 12000 = ₹24,000.
A and B start a business with investments of ₹8,000 and ₹12,000 respectively. At the end of the year, they incur a loss of ₹5,000. How much loss does B bear?
- ₹4,000
- ₹3,000
- ₹2,000
- ₹2,500
Explanation: Loss sharing ratio = 8000:12000 = 2:3. B's share = (3/5)×5000 = ₹3,000.
A invests ₹5,000 for the whole year. B invests ₹8,000 for the first 6 months and ₹6,000 for the next 6 months. C joins after 6 months with ₹10,000. If the profit is ₹17,000, what is B's share?
- ₹5,000
- ₹4,600
- ₹7,000
- ₹6,000
Explanation: A = 5000×12 = 60,000. B = 8000×6 + 6000×6 = 84,000. C = 10000×6 = 60,000. Ratio = 60:84:60 = 5:7:5. Total = 17. B's share = (7/17)×17000 = ₹7,000.
A and B invest ₹12,000 and ₹18,000 respectively in a business. If the profit is 25% of the total investment, what is A's share of the profit?
- ₹3,000
- ₹2,500
- ₹7,500
- ₹4,500
Explanation: Total investment = 12000 + 18000 = ₹30,000. Profit = 25% of 30000 = ₹7,500. Capital ratio = 12:18 = 2:3. A's share = (2/5)×7500 = ₹3,000.
A starts a business with ₹5,000 and adds ₹1,000 every month for 12 months. B starts with ₹8,000 and adds ₹500 every month for 12 months. What is the ratio of their equivalent investments?
Explanation: A's investments form an AP: 5000, 6000, ..., 16000. Sum = 12/2 × (5000+16000) = ₹1,26,000. B's investments: 8000, 8500, ..., 13500. Sum = 12/2 × (8000+13500) = ₹1,29,000. Ratio = 126000:129000 = 42:43.
A container contains 80 litres of milk. 20 litres is drawn out and replaced with water. This process is repeated once more. What is the ratio of milk to water in the final mixture?
Explanation: After 1st replacement: Milk = 80×(60/80) = 60L. After 2nd replacement: Milk = 60×(60/80) = 45L. Water = 80-45 = 35L. Ratio = 45:35 = 9:7.
If a:b = 2:3, b:c = 3:4, and c:d = 4:5, what is the ratio a:d?
Explanation: a:b:c:d = 2:3:4:5 (by chaining). Therefore a:d = 2:5.
If x is the sub-duplicate ratio of 9:16, and y is the duplicate ratio of 2:3, what is the ratio x:y?
Explanation: Sub-duplicate ratio of 9:16 = √9:√16 = 3:4. Duplicate ratio of 2:3 = 2²:3² = 4:9. x:y = 3/4 : 4/9 = 27:16.
What is the ratio of the third proportional to 4 and 6, to the mean proportional between 9 and 16?
Explanation: Third proportional to 4 and 6: 4/6 = 6/x, so x = 36/4 = 9. Mean proportional between 9 and 16 = √(9×16) = 12. Ratio = 9:12 = 3:4.
The ratio of A to B is 2:3 and the ratio of B to C is 4:5. If A is 40% of D, what is the ratio of C to D?
Explanation: A:B:C = 8:12:15. A = 40% of D = 2D/5. If A = 8, then 8 = 2D/5, so D = 20. C:D = 15:20 = 3:4.
A invests ₹10,000 which earns 20% simple interest per annum for 2 years. B invests ₹10,000 which earns 20% compound interest per annum for 2 years. They then enter a partnership with these accumulated amounts. If the profit is ₹7,100, what is the difference between their shares?
Explanation: A's capital = 10000 + (10000×20%×2) = ₹14,000. B's capital = 10000×(1.2)² = ₹14,400. Ratio = 14000:14400 = 35:36. Total = 71. Difference = (1/71)×7100 = ₹100.
8 men and 12 boys can complete a piece of work in 5 days. 6 men and 8 boys can complete the same work in 7 days. What is the ratio of the efficiency of a man to that of a boy?
Explanation: Let a man's daily work = m, a boy's = b. Total work = (8m+12b)×5 = (6m+8b)×7. So 40m+60b = 42m+56b, giving 4b = 2m, so m/b = 2/1. Ratio = 2:1.
A and B start a business with ₹20,000 and ₹30,000 respectively. B gives A a personal loan of ₹10,000 at 10% simple interest per annum. If the annual profit from the business is ₹15,000 (before any interest adjustment), what is A's net gain?
- ₹5,000
- ₹6,000
- ₹4,000
- ₹7,000
Explanation: Capital ratio = 20000:30000 = 2:3. A's profit share = (2/5)×15000 = ₹6,000. Interest on loan = 10% of 10000 = ₹1,000. A's net gain = 6000 - 1000 = ₹5,000.
A works 8 hours per day for 5 days a week. B works 6 hours per day for 6 days a week. If their hourly wages are the same, what is the ratio of their monthly wages (assuming 4 weeks per month)?
Explanation: A's monthly hours = 8×5×4 = 160. B's monthly hours = 6×6×4 = 144. Ratio = 160:144 = 10:9.
The ratio of the speed of a boat in still water to the speed of the stream is 5:1. What is the ratio of the time taken to travel a certain distance upstream to the time taken to travel the same distance downstream?
Explanation: Let boat speed = 5x, stream = x. Upstream speed = 4x, downstream = 6x. Time is inversely proportional to speed. Time ratio = 1/4x : 1/6x = 6:4 = 3:2.
A and B invest ₹10,000 and ₹15,000 in a business. The profit is ₹12,000. They decide to reinvest 50% of the profit in the business in the ratio 2:3 and withdraw the remaining profit. How much does A withdraw?
- ₹4,800
- ₹1,200
- ₹3,600
- ₹2,400
Explanation: Capital ratio = 10000:15000 = 2:3. A's share = (2/5)×12000 = ₹4,800. Total reinvestment = 50% of 12000 = ₹6,000. A's reinvestment = (2/5)×6000 = ₹2,400. A's withdrawal = 4800 - 2400 = ₹2,400.
In an examination, three students A, B, and C score marks in the ratio 3:4:5. If A scores 45% and B scores 60% of the maximum marks (which is the same for all), and their total marks are 360, what is C's score?
Explanation: Marks ratio = 3:4:5. Total = 360. C's marks = (5/12)×360 = 150. Check: A = 90 = 45% of 200, B = 120 = 60% of 200, C = 150 = 75% of 200.
A's monthly income is ₹15,000 and B's is ₹20,000. If A pays 10% income tax and B pays 15% income tax, what is the ratio of their disposable incomes?
Explanation: A's disposable income = 15000 - 10% of 15000 = ₹13,500. B's disposable = 20000 - 15% of 20000 = ₹17,000. Ratio = 13500:17000 = 27:34.
Two varieties of rice costing ₹40 per kg and ₹60 per kg are mixed in the ratio 3:2. What is the cost per kg of the mixed rice?
Explanation: Cost of mixture = (3×40 + 2×60)/(3+2) = (120+120)/5 = ₹48 per kg.
A invests ₹8,000 for 12 months, B invests ₹12,000 for 8 months, and C invests ₹15,000 for 6 months. If the profit is ₹14,100, what is B's share?
- ₹4,600
- ₹7,000
- ₹5,000
- ₹4,500
Explanation: A = 8000×12 = 96,000. B = 12000×8 = 96,000. C = 15000×6 = 90,000. Ratio = 96:96:90 = 16:16:15. Total = 47. B's share = (16/47)×14100 = ₹7,000.
The present age of a father and his son are in the ratio 5:2. After 8 years, the ratio of their ages will be 2:1. What is the father's present age?
- 48 years
- 32 years
- 40 years
- 56 years
Explanation: Let present ages be 5x and 2x. After 8 years: (5x+8)/(2x+8) = 2/1. So 5x+8 = 4x+16, giving x = 8. Father's age = 5×8 = 40 years.
A trader marks his goods 40% above the cost price and then allows a discount of 20% on the marked price. What is the ratio of his profit to the cost price?
Explanation: Let CP = ₹100. MP = ₹140. SP = 140 - 20% of 140 = ₹112. Profit = ₹12. Profit:CP = 12:100 = 3:25.
A and B invest ₹15,000 and ₹10,000 respectively. A manages the business and gets 10% of the profit as commission. The remaining profit is divided in the ratio of their capitals. If the total profit is ₹25,000, what is A's total share?
- ₹16,000
- ₹15,000
- ₹14,000
- ₹13,500
Explanation: Commission = 10% of 25000 = ₹2,500. Remaining = ₹22,500. Capital ratio = 15000:10000 = 3:2. A's capital share = (3/5)×22500 = ₹13,500. A's total = 2500 + 13500 = ₹16,000.
A 60-litre mixture contains 25% water and the rest milk. How many litres of pure water must be added to make the mixture 50% water?
- 15 litres
- 40 litres
- 20 litres
- 30 litres
Explanation: Current water = 25% of 60 = 15L. Let x litres water be added. (15+x)/(60+x) = 1/2. 30+2x = 60+x, so x = 30. Check: 45L water in 90L = 50%.
In an election, 8% of the votes are invalid. Candidate A gets 55% of the valid votes. If the total number of votes is 15,000, what is the ratio of votes received by A to the total votes cast?
- 11:20
- 500:253
- 253:500
- 253:250
Explanation: Valid votes = 92% of 15000 = 13,800. A's votes = 55% of 13800 = 7,590. Ratio = 7590:15000 = 253:500.
A and B invest ₹10,000 and ₹20,000 in a business. They decide to donate 10% of the profit to charity and divide the rest in the ratio of their capitals. If the profit is ₹33,000, what is B's share?
- ₹18,800
- ₹19,800
- ₹20,600
- ₹22,000
Explanation: Charity = 10% of 33000 = ₹3,300. Remaining = ₹29,700. Capital ratio = 10000:20000 = 1:2. B's share = (2/3)×29700 = ₹19,800.
The marked price of an article is ₹800. It is sold after two successive discounts of 20% and 10%. What is the ratio of the selling price to the marked price?
Explanation: After 1st discount: 800 × 0.80 = ₹640. After 2nd discount: 640 × 0.90 = ₹576. Ratio = 576:800 = 18:25.
The population of a town is 50,000 with the ratio of males to females being 3:2. If the male population increases by 10% and the female population increases by 20%, what is the new ratio of males to females?
Explanation: Males = 3/5 × 50000 = 30,000. Females = 20,000. New males = 30,000 × 1.10 = 33,000. New females = 20,000 × 1.20 = 24,000. Ratio = 33:24 = 11:8.
A and B invest ₹25,000 and ₹35,000 respectively in a business. If the annual profit is ₹18,000, what is the ratio of A's profit share to A's investment?
Explanation: Capital ratio = 25000:35000 = 5:7. A's profit = (5/12)×18000 = ₹7,500. Ratio of A's profit to investment = 7500:25000 = 3:10.