Time and Work Competitive Exams
100 questions · Mathematics
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Question 1 of 100
A, B, and C can complete a piece of work in 12, 18, and 36 days respectively. They undertake the work together for a total payment of Rs. 6,600. What is A's share?
ExplanationWages are divided in proportion to each person's work rate. A's share = Total x (1/12) / [(1/12)+(1/18)+(1/36)] = Rs. 3,300.
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Question 2 of 100
A can complete a work in 9 days and B can complete it in 12 days. A starts the work alone and works for 4 days, after which B takes over and finishes the remaining work alone. In how many days does B finish the remaining work?
ExplanationWork done by A in 4 days = 4/9 = 4/9. Remaining work = 5/9. Time for B to finish remaining work = remaining / (1/12) = 6 2/3 days.
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Question 3 of 100
A can complete a work in 12 days and B can complete it in 18 days. A starts the work alone and works for 5 days, after which B takes over and finishes the remaining work alone. In how many days does B finish the remaining work?
ExplanationWork done by A in 5 days = 5/12 = 5/12. Remaining work = 7/12. Time for B to finish remaining work = remaining / (1/18) = 10 1/2 days.
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Question 4 of 100
A, B, and C can individually complete a task in 9, 18, and 36 days respectively. Working together, in how many days will they finish the task?
ExplanationCombined 1-day work = 1/9+1/18+1/36 = 7/36. Time together = 1/(combined rate) = 5 1/7 days.
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Question 5 of 100
A can complete a piece of work in 24 days. A and B working together can complete the same work in 16 days. In how many days can B alone complete the work?
ExplanationB's 1-day work = 1/16 - 1/24 = 1/48. So B alone takes 48 days.
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Question 6 of 100
15 men working 6 hours per day can complete a job in 10 days. In how many days can 12 men, working 5 hours per day, complete the same job?
ExplanationTotal work = M1 x D1 x H1 = 15 x 10 x 6 = 900 man-hours. Days for M2 men at H2 hours/day = 900/(12x5) = 15 days.
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Question 7 of 100
A can complete a work in 20 days and B can complete it in 30 days. They work on alternate days, with A starting first (A works on day 1, B on day 2, and so on). In how many days will the work be completed?
ExplanationIn each 2-day cycle (A then B), work done = 1/20+1/30 = 1/12. After counting full cycles and the remaining fraction of work, total time = 24 days.
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Question 8 of 100
12 men working 4 hours per day can complete a job in 15 days. In how many days can 10 men, working 6 hours per day, complete the same job?
ExplanationTotal work = M1 x D1 x H1 = 12 x 15 x 4 = 720 man-hours. Days for M2 men at H2 hours/day = 720/(10x6) = 12 days.
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Question 9 of 100
A can do a piece of work in 20 days and B can do it in 30 days. They complete the work together and are paid Rs. 10,000 in total. What is A's share of the payment?
ExplanationWages are shared in the ratio of work done, i.e., in the ratio of their rates: (1/20):(1/30) = 30:20. A's share = Total x 30/(20+30) = Rs. 6,000.
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Question 10 of 100
Pipe A can fill a tank in 15 hours and Pipe B can fill the same tank in 25 hours. If both pipes are opened together, in how much time will the tank be filled?
ExplanationCombined rate = 1/15 + 1/25. Time to fill = 1/(combined rate) = 9 3/8 hours.
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Question 11 of 100
A can complete a piece of work in 6 days and B can complete it in 9 days. In how many days can they complete it working together?
ExplanationCombined 1-day work = 1/6 + 1/9 = 5/18. Time together = 1 / (combined rate) = 3 3/5 days.
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Question 12 of 100
Two inlet pipes can individually fill a tank in 15 hours and 20 hours, while an outlet pipe can empty the full tank in 60 hours. If all three pipes are opened together, in how much time will the tank be filled?
ExplanationNet rate = 1/15 + 1/20 - 1/60 = 1/10. Time to fill = 1/(net rate) = 10 hours.
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Question 13 of 100
A can complete a work in 15 days and B can complete it in 20 days. A starts the work alone and works for 6 days, after which B takes over and finishes the remaining work alone. In how many days does B finish the remaining work?
ExplanationWork done by A in 6 days = 6/15 = 2/5. Remaining work = 3/5. Time for B to finish remaining work = remaining / (1/20) = 12 days.
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Question 14 of 100
A can complete a work in 14 days and B can complete it in 21 days. They work on alternate days, with A starting first (A works on day 1, B on day 2, and so on). In how many days will the work be completed?
ExplanationIn each 2-day cycle (A then B), work done = 1/14+1/21 = 5/42. After counting full cycles and the remaining fraction of work, total time = 16 2/3 days.
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Question 15 of 100
A is 60% more efficient than B. If B alone takes 16 days to complete a task, how many days will A alone take?
ExplanationA's rate is 60% more than B's: A's 1-day work = (1/16) x (100+60)/100. A's time = 1/(A's rate) = 10 days.
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Question 16 of 100
A can complete a piece of work in 12 days. A and B working together can complete the same work in 8 days. In how many days can B alone complete the work?
ExplanationB's 1-day work = 1/8 - 1/12 = 1/24. So B alone takes 24 days.
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Question 17 of 100
20 men can complete a piece of work in 10 days. In how many days can 25 men complete the same work, assuming the same daily working hours and individual efficiency?
ExplanationTotal work (in man-days) = 20 x 10 = 200 man-days. Days needed for 25 men = 200/25 = 8 days.
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Question 18 of 100
Two inlet pipes can individually fill a tank in 10 hours and 15 hours, while an outlet pipe can empty the full tank in 30 hours. If all three pipes are opened together, in how much time will the tank be filled?
ExplanationNet rate = 1/10 + 1/15 - 1/30 = 2/15. Time to fill = 1/(net rate) = 7 1/2 hours.
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Question 19 of 100
A is 20% more efficient than B. If B alone takes 25 days to complete a task, how many days will A alone take?
ExplanationA's rate is 20% more than B's: A's 1-day work = (1/25) x (100+20)/100. A's time = 1/(A's rate) = 20 5/6 days.
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Question 20 of 100
An inlet pipe can fill a tank in 10 hours, while an outlet pipe can empty the full tank in 15 hours. If both pipes are opened together (tank initially empty), in how much time will the tank be filled?
ExplanationNet filling rate per hour = 1/10 - 1/15 = 1/30. Time to fill = 1/(net rate) = 30 hours.
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Question 21 of 100
A can complete a work in 8 days and B can complete it in 12 days. A starts the work alone and works for 3 days, after which B takes over and finishes the remaining work alone. In how many days does B finish the remaining work?
ExplanationWork done by A in 3 days = 3/8 = 3/8. Remaining work = 5/8. Time for B to finish remaining work = remaining / (1/12) = 7 1/2 days.
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Question 22 of 100
A can complete a work in 8 days and B can complete it in 12 days. They work on alternate days, with A starting first (A works on day 1, B on day 2, and so on). In how many days will the work be completed?
ExplanationIn each 2-day cycle (A then B), work done = 1/8+1/12 = 5/24. After counting full cycles and the remaining fraction of work, total time = 9 1/2 days.
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Question 23 of 100
An inlet pipe can fill a tank in 12 hours, while an outlet pipe can empty the full tank in 20 hours. If both pipes are opened together (tank initially empty), in how much time will the tank be filled?
ExplanationNet filling rate per hour = 1/12 - 1/20 = 1/30. Time to fill = 1/(net rate) = 30 hours.
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Question 24 of 100
A is 3 times as efficient as B. If B alone can complete a piece of work in 30 days, in how many days can A alone complete the same work?
ExplanationSince A is 3 times as efficient, A takes 1/3 of B's time: 30/3 = 10 days.
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Question 25 of 100
A, B, and C can individually complete a task in 10, 15, and 30 days respectively. Working together, in how many days will they finish the task?
ExplanationCombined 1-day work = 1/10+1/15+1/30 = 1/5. Time together = 1/(combined rate) = 5 days.
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Question 26 of 100
20 men working 5 hours per day can complete a job in 8 days. In how many days can 16 men, working 10 hours per day, complete the same job?
ExplanationTotal work = M1 x D1 x H1 = 20 x 8 x 5 = 800 man-hours. Days for M2 men at H2 hours/day = 800/(16x10) = 5 days.
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Question 27 of 100
A is 5 times as efficient as B. If B alone can complete a piece of work in 25 days, in how many days can A alone complete the same work?
ExplanationSince A is 5 times as efficient, A takes 1/5 of B's time: 25/5 = 5 days.
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Question 28 of 100
A can complete a piece of work in 10 days and B can complete it in 25 days. In how many days can they complete it working together?
ExplanationCombined 1-day work = 1/10 + 1/25 = 7/50. Time together = 1 / (combined rate) = 7 1/7 days.
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Question 29 of 100
An inlet pipe can fill a tank in 20 hours, while an outlet pipe can empty the full tank in 30 hours. If both pipes are opened together (tank initially empty), in how much time will the tank be filled?
ExplanationNet filling rate per hour = 1/20 - 1/30 = 1/60. Time to fill = 1/(net rate) = 60 hours.
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Question 30 of 100
10 men can complete a piece of work in 20 days. In how many days can 5 men complete the same work, assuming the same daily working hours and individual efficiency?
ExplanationTotal work (in man-days) = 10 x 20 = 200 man-days. Days needed for 5 men = 200/5 = 40 days.
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Question 31 of 100
Pipe A can fill a tank in 8 hours and Pipe B can fill the same tank in 24 hours. If both pipes are opened together, in how much time will the tank be filled?
ExplanationCombined rate = 1/8 + 1/24. Time to fill = 1/(combined rate) = 6 hours.
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Question 32 of 100
Pipe A can fill a tank in 9 hours and Pipe B can fill the same tank in 27 hours. If both pipes are opened together, in how much time will the tank be filled?
ExplanationCombined rate = 1/9 + 1/27. Time to fill = 1/(combined rate) = 6 3/4 hours.
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Question 33 of 100
A is 3 times as efficient as B. If B alone can complete a piece of work in 24 days, in how many days can A alone complete the same work?
ExplanationSince A is 3 times as efficient, A takes 1/3 of B's time: 24/3 = 8 days.
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Question 34 of 100
18 men can complete a piece of work in 12 days. In how many days can 9 men complete the same work, assuming the same daily working hours and individual efficiency?
ExplanationTotal work (in man-days) = 18 x 12 = 216 man-days. Days needed for 9 men = 216/9 = 24 days.
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Question 35 of 100
A can complete a piece of work in 12 days and B can complete it in 18 days. In how many days can they complete it working together?
ExplanationCombined 1-day work = 1/12 + 1/18 = 5/36. Time together = 1 / (combined rate) = 7 1/5 days.
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Question 36 of 100
A is 50% more efficient than B. If B alone takes 15 days to complete a task, how many days will A alone take?
ExplanationA's rate is 50% more than B's: A's 1-day work = (1/15) x (100+50)/100. A's time = 1/(A's rate) = 10 days.
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Question 37 of 100
10 men working 8 hours per day can complete a job in 12 days. In how many days can 8 men, working 10 hours per day, complete the same job?
ExplanationTotal work = M1 x D1 x H1 = 10 x 12 x 8 = 960 man-hours. Days for M2 men at H2 hours/day = 960/(8x10) = 12 days.
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Question 38 of 100
15 men can complete a piece of work in 16 days. In how many days can 12 men complete the same work, assuming the same daily working hours and individual efficiency?
ExplanationTotal work (in man-days) = 15 x 16 = 240 man-days. Days needed for 12 men = 240/12 = 20 days.
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Question 39 of 100
A, B, and C can complete a piece of work in 10, 15, and 30 days respectively. They undertake the work together for a total payment of Rs. 7,700. What is A's share?
ExplanationWages are divided in proportion to each person's work rate. A's share = Total x (1/10) / [(1/10)+(1/15)+(1/30)] = Rs. 3,850.
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Question 40 of 100
An inlet pipe can fill a tank in 18 hours, while an outlet pipe can empty the full tank in 27 hours. If both pipes are opened together (tank initially empty), in how much time will the tank be filled?
ExplanationNet filling rate per hour = 1/18 - 1/27 = 1/54. Time to fill = 1/(net rate) = 54 hours.
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Question 41 of 100
A can do a piece of work in 15 days and B can do it in 20 days. They complete the work together and are paid Rs. 7,000 in total. What is A's share of the payment?
ExplanationWages are shared in the ratio of work done, i.e., in the ratio of their rates: (1/15):(1/20) = 20:15. A's share = Total x 20/(15+20) = Rs. 4,000.
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Question 42 of 100
A can do a piece of work in 9 days and B can do it in 12 days. They complete the work together and are paid Rs. 4,200 in total. What is A's share of the payment?
ExplanationWages are shared in the ratio of work done, i.e., in the ratio of their rates: (1/9):(1/12) = 12:9. A's share = Total x 12/(9+12) = Rs. 2,400.
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Question 43 of 100
If A is twice as efficient as B, and B takes 'x' days to complete a task alone, how long will A take to complete it alone?
ExplanationBeing twice as efficient means A completes the work in half the time B would take.
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Question 44 of 100
A can complete a piece of work in 20 days. A and B working together can complete the same work in 12 days. In how many days can B alone complete the work?
ExplanationB's 1-day work = 1/12 - 1/20 = 1/30. So B alone takes 30 days.
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Question 45 of 100
An inlet pipe can fill a tank in 9 hours, while an outlet pipe can empty the full tank in 15 hours. If both pipes are opened together (tank initially empty), in how much time will the tank be filled?
ExplanationNet filling rate per hour = 1/9 - 1/15 = 2/45. Time to fill = 1/(net rate) = 22 1/2 hours.
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Question 46 of 100
12 men can complete a piece of work in 15 days. In how many days can 10 men complete the same work, assuming the same daily working hours and individual efficiency?
ExplanationTotal work (in man-days) = 12 x 15 = 180 man-days. Days needed for 10 men = 180/10 = 18 days.
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Question 47 of 100
A, B, and C can individually complete a task in 12, 18, and 36 days respectively. Working together, in how many days will they finish the task?
ExplanationCombined 1-day work = 1/12+1/18+1/36 = 1/6. Time together = 1/(combined rate) = 6 days.
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Question 48 of 100
25 men can complete a piece of work in 8 days. In how many days can 20 men complete the same work, assuming the same daily working hours and individual efficiency?
ExplanationTotal work (in man-days) = 25 x 8 = 200 man-days. Days needed for 20 men = 200/20 = 10 days.
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Question 49 of 100
A, B, and C can individually complete a task in 10, 20, and 30 days respectively. Working together, in how many days will they finish the task?
ExplanationCombined 1-day work = 1/10+1/20+1/30 = 11/60. Time together = 1/(combined rate) = 5 5/11 days.
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Question 50 of 100
8 men can complete a piece of work in 24 days. In how many days can 6 men complete the same work, assuming the same daily working hours and individual efficiency?
ExplanationTotal work (in man-days) = 8 x 24 = 192 man-days. Days needed for 6 men = 192/6 = 32 days.
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Question 51 of 100
A is 25% more efficient than B. If B alone takes 20 days to complete a task, how many days will A alone take?
ExplanationA's rate is 25% more than B's: A's 1-day work = (1/20) x (100+25)/100. A's time = 1/(A's rate) = 16 days.
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Question 52 of 100
A, B, and C can individually complete a task in 6, 12, and 24 days respectively. Working together, in how many days will they finish the task?
ExplanationCombined 1-day work = 1/6+1/12+1/24 = 7/24. Time together = 1/(combined rate) = 3 3/7 days.
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Question 53 of 100
A is 3 times as efficient as B. If B alone can complete a piece of work in 18 days, in how many days can A alone complete the same work?
ExplanationSince A is 3 times as efficient, A takes 1/3 of B's time: 18/3 = 6 days.
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Question 54 of 100
A can do a piece of work in 6 days and B can do it in 9 days. They complete the work together and are paid Rs. 3,000 in total. What is A's share of the payment?
ExplanationWages are shared in the ratio of work done, i.e., in the ratio of their rates: (1/6):(1/9) = 9:6. A's share = Total x 9/(6+9) = Rs. 1,800.
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Question 55 of 100
An inlet pipe can fill a tank in 8 hours, while an outlet pipe can empty the full tank in 12 hours. If both pipes are opened together (tank initially empty), in how much time will the tank be filled?
ExplanationNet filling rate per hour = 1/8 - 1/12 = 1/24. Time to fill = 1/(net rate) = 24 hours.
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Question 56 of 100
A is 2 times as efficient as B. If B alone can complete a piece of work in 20 days, in how many days can A alone complete the same work?
ExplanationSince A is 2 times as efficient, A takes 1/2 of B's time: 20/2 = 10 days.
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Question 57 of 100
A can complete a piece of work in 30 days. A and B working together can complete the same work in 20 days. In how many days can B alone complete the work?
ExplanationB's 1-day work = 1/20 - 1/30 = 1/60. So B alone takes 60 days.
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Question 58 of 100
A can complete a piece of work in 15 days. A and B working together can complete the same work in 10 days. In how many days can B alone complete the work?
ExplanationB's 1-day work = 1/10 - 1/15 = 1/30. So B alone takes 30 days.
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Question 59 of 100
16 men can complete a piece of work in 18 days. In how many days can 12 men complete the same work, assuming the same daily working hours and individual efficiency?
ExplanationTotal work (in man-days) = 16 x 18 = 288 man-days. Days needed for 12 men = 288/12 = 24 days.
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Question 60 of 100
Pipe A can fill a tank in 6 hours and Pipe B can fill the same tank in 18 hours. If both pipes are opened together, in how much time will the tank be filled?
ExplanationCombined rate = 1/6 + 1/18. Time to fill = 1/(combined rate) = 4 1/2 hours.
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Question 61 of 100
A is 2 times as efficient as B. If B alone can complete a piece of work in 15 days, in how many days can A alone complete the same work?
ExplanationSince A is 2 times as efficient, A takes 1/2 of B's time: 15/2 = 7 1/2 days.
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Question 62 of 100
Pipe A can fill a tank in 12 hours and Pipe B can fill the same tank in 20 hours. If both pipes are opened together, in how much time will the tank be filled?
ExplanationCombined rate = 1/12 + 1/20. Time to fill = 1/(combined rate) = 7 1/2 hours.
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Question 63 of 100
A can complete a piece of work in 18 days and B can complete it in 27 days. In how many days can they complete it working together?
ExplanationCombined 1-day work = 1/18 + 1/27 = 5/54. Time together = 1 / (combined rate) = 10 4/5 days.
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Question 64 of 100
25 men working 8 hours per day can complete a job in 6 days. In how many days can 20 men, working 10 hours per day, complete the same job?
ExplanationTotal work = M1 x D1 x H1 = 25 x 6 x 8 = 1200 man-hours. Days for M2 men at H2 hours/day = 1200/(20x10) = 6 days.
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Question 65 of 100
A, B, and C can individually complete a task in 8, 12, and 24 days respectively. Working together, in how many days will they finish the task?
ExplanationCombined 1-day work = 1/8+1/12+1/24 = 1/4. Time together = 1/(combined rate) = 4 days.
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Question 66 of 100
A can complete a piece of work in 18 days. A and B working together can complete the same work in 12 days. In how many days can B alone complete the work?
ExplanationB's 1-day work = 1/12 - 1/18 = 1/36. So B alone takes 36 days.
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Question 67 of 100
A can complete a work in 20 days and B can complete it in 30 days. A starts the work alone and works for 10 days, after which B takes over and finishes the remaining work alone. In how many days does B finish the remaining work?
ExplanationWork done by A in 10 days = 10/20 = 1/2. Remaining work = 1/2. Time for B to finish remaining work = remaining / (1/30) = 15 days.
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Question 68 of 100
A can complete a work in 6 days and B can complete it in 9 days. They work on alternate days, with A starting first (A works on day 1, B on day 2, and so on). In how many days will the work be completed?
ExplanationIn each 2-day cycle (A then B), work done = 1/6+1/9 = 5/18. After counting full cycles and the remaining fraction of work, total time = 7 days.
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Question 69 of 100
In a 'pipes and cisterns' problem, if an outlet pipe (which empties a tank) works alongside an inlet pipe (which fills it), the net rate of filling is found by:
ExplanationSince the outlet pipe works against the filling process, its rate is subtracted from the inlet pipe's rate to find the net filling rate.
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Question 70 of 100
A can complete a piece of work in 14 days and B can complete it in 21 days. In how many days can they complete it working together?
ExplanationCombined 1-day work = 1/14 + 1/21 = 5/42. Time together = 1 / (combined rate) = 8 2/5 days.
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Question 71 of 100
A can complete a work in 12 days and B can complete it in 18 days. They work on alternate days, with A starting first (A works on day 1, B on day 2, and so on). In how many days will the work be completed?
ExplanationIn each 2-day cycle (A then B), work done = 1/12+1/18 = 5/36. After counting full cycles and the remaining fraction of work, total time = 14 1/3 days.
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Question 72 of 100
A can complete a piece of work in 16 days and B can complete it in 24 days. In how many days can they complete it working together?
ExplanationCombined 1-day work = 1/16 + 1/24 = 5/48. Time together = 1 / (combined rate) = 9 3/5 days.
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Question 73 of 100
Pipe A can fill a tank in 20 hours and Pipe B can fill the same tank in 60 hours. If both pipes are opened together, in how much time will the tank be filled?
ExplanationCombined rate = 1/20 + 1/60. Time to fill = 1/(combined rate) = 15 hours.
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Question 74 of 100
In problems combining the work rates of two people working together, the correct approach is to:
ExplanationWork rates (not the number of days) are additive; the combined time is the reciprocal of the sum of the individual rates.
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Question 75 of 100
A can complete a work in 10 days and B can complete it in 15 days. They work on alternate days, with A starting first (A works on day 1, B on day 2, and so on). In how many days will the work be completed?
ExplanationIn each 2-day cycle (A then B), work done = 1/10+1/15 = 1/6. After counting full cycles and the remaining fraction of work, total time = 12 days.
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Question 76 of 100
A can complete a piece of work in 20 days and B can complete it in 30 days. In how many days can they complete it working together?
ExplanationCombined 1-day work = 1/20 + 1/30 = 1/12. Time together = 1 / (combined rate) = 12 days.
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Question 77 of 100
A is 4 times as efficient as B. If B alone can complete a piece of work in 20 days, in how many days can A alone complete the same work?
ExplanationSince A is 4 times as efficient, A takes 1/4 of B's time: 20/4 = 5 days.
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Question 78 of 100
If A can complete a piece of work in 'n' days, A's one-day work (work rate) is:
ExplanationIf a task takes n days to complete at a constant rate, the fraction of work done in a single day is 1/n.
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Question 79 of 100
Pipe A can fill a tank in 10 hours and Pipe B can fill the same tank in 30 hours. If both pipes are opened together, in how much time will the tank be filled?
ExplanationCombined rate = 1/10 + 1/30. Time to fill = 1/(combined rate) = 7 1/2 hours.
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Question 80 of 100
A can complete a piece of work in 10 days. A and B working together can complete the same work in 6 days. In how many days can B alone complete the work?
ExplanationB's 1-day work = 1/6 - 1/10 = 1/15. So B alone takes 15 days.
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Question 81 of 100
A can complete a piece of work in 9 days and B can complete it in 12 days. In how many days can they complete it working together?
ExplanationCombined 1-day work = 1/9 + 1/12 = 7/36. Time together = 1 / (combined rate) = 5 1/7 days.
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Question 82 of 100
A can complete a piece of work in 24 days and B can complete it in 36 days. In how many days can they complete it working together?
ExplanationCombined 1-day work = 1/24 + 1/36 = 5/72. Time together = 1 / (combined rate) = 14 2/5 days.
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Question 83 of 100
A can complete a piece of work in 8 days and B can complete it in 12 days. In how many days can they complete it working together?
ExplanationCombined 1-day work = 1/8 + 1/12 = 5/24. Time together = 1 / (combined rate) = 4 4/5 days.
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Question 84 of 100
A can complete a work in 10 days and B can complete it in 15 days. A starts the work alone and works for 4 days, after which B takes over and finishes the remaining work alone. In how many days does B finish the remaining work?
ExplanationWork done by A in 4 days = 4/10 = 2/5. Remaining work = 3/5. Time for B to finish remaining work = remaining / (1/15) = 9 days.
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Question 85 of 100
A can complete a piece of work in 40 days. A and B working together can complete the same work in 24 days. In how many days can B alone complete the work?
ExplanationB's 1-day work = 1/24 - 1/40 = 1/60. So B alone takes 60 days.
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Question 86 of 100
Two inlet pipes can individually fill a tank in 8 hours and 12 hours, while an outlet pipe can empty the full tank in 24 hours. If all three pipes are opened together, in how much time will the tank be filled?
ExplanationNet rate = 1/8 + 1/12 - 1/24 = 1/6. Time to fill = 1/(net rate) = 6 hours.
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Question 87 of 100
A can do a piece of work in 10 days and B can do it in 15 days. They complete the work together and are paid Rs. 5,000 in total. What is A's share of the payment?
ExplanationWages are shared in the ratio of work done, i.e., in the ratio of their rates: (1/10):(1/15) = 15:10. A's share = Total x 15/(10+15) = Rs. 3,000.
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Question 88 of 100
A, B, and C can individually complete a task in 15, 20, and 60 days respectively. Working together, in how many days will they finish the task?
ExplanationCombined 1-day work = 1/15+1/20+1/60 = 2/15. Time together = 1/(combined rate) = 7 1/2 days.
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Question 89 of 100
A is 2 times as efficient as B. If B alone can complete a piece of work in 18 days, in how many days can A alone complete the same work?
ExplanationSince A is 2 times as efficient, A takes 1/2 of B's time: 18/2 = 9 days.
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Question 90 of 100
A, B, and C can individually complete a task in 20, 30, and 60 days respectively. Working together, in how many days will they finish the task?
ExplanationCombined 1-day work = 1/20+1/30+1/60 = 1/10. Time together = 1/(combined rate) = 10 days.
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Question 91 of 100
A can complete a piece of work in 15 days and B can complete it in 20 days. In how many days can they complete it working together?
ExplanationCombined 1-day work = 1/15 + 1/20 = 7/60. Time together = 1 / (combined rate) = 8 4/7 days.
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Question 92 of 100
Pipe A can fill a tank in 10 hours and Pipe B can fill the same tank in 15 hours. If both pipes are opened together, in how much time will the tank be filled?
ExplanationCombined rate = 1/10 + 1/15. Time to fill = 1/(combined rate) = 6 hours.
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Question 93 of 100
A can do a piece of work in 12 days and B can do it in 18 days. They complete the work together and are paid Rs. 6,000 in total. What is A's share of the payment?
ExplanationWages are shared in the ratio of work done, i.e., in the ratio of their rates: (1/12):(1/18) = 18:12. A's share = Total x 18/(12+18) = Rs. 3,600.
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Question 94 of 100
Two inlet pipes can individually fill a tank in 12 hours and 20 hours, while an outlet pipe can empty the full tank in 30 hours. If all three pipes are opened together, in how much time will the tank be filled?
ExplanationNet rate = 1/12 + 1/20 - 1/30 = 1/10. Time to fill = 1/(net rate) = 10 hours.
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Question 95 of 100
A is 100% more efficient than B. If B alone takes 10 days to complete a task, how many days will A alone take?
ExplanationA's rate is 100% more than B's: A's 1-day work = (1/10) x (100+100)/100. A's time = 1/(A's rate) = 5 days.
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Question 96 of 100
A can complete a piece of work in 10 days and B can complete it in 15 days. In how many days can they complete it working together?
ExplanationCombined 1-day work = 1/10 + 1/15 = 1/6. Time together = 1 / (combined rate) = 6 days.
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Question 97 of 100
A is 40% more efficient than B. If B alone takes 14 days to complete a task, how many days will A alone take?
ExplanationA's rate is 40% more than B's: A's 1-day work = (1/14) x (100+40)/100. A's time = 1/(A's rate) = 10 days.
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Question 98 of 100
An inlet pipe can fill a tank in 15 hours, while an outlet pipe can empty the full tank in 25 hours. If both pipes are opened together (tank initially empty), in how much time will the tank be filled?
ExplanationNet filling rate per hour = 1/15 - 1/25 = 2/75. Time to fill = 1/(net rate) = 37 1/2 hours.
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Question 99 of 100
A can do a piece of work in 8 days and B can do it in 12 days. They complete the work together and are paid Rs. 4,000 in total. What is A's share of the payment?
ExplanationWages are shared in the ratio of work done, i.e., in the ratio of their rates: (1/8):(1/12) = 12:8. A's share = Total x 12/(8+12) = Rs. 2,400.
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Question 100 of 100
Two inlet pipes can individually fill a tank in 10 hours and 12 hours, while an outlet pipe can empty the full tank in 15 hours. If all three pipes are opened together, in how much time will the tank be filled?
ExplanationNet rate = 1/10 + 1/12 - 1/15 = 7/60. Time to fill = 1/(net rate) = 8 4/7 hours.
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