IPMPrepA and B together finish a job in 37742 days; A alone takes 13 days. How long would B take alone?
Solution
B's rate = 42377 − 113 = 129.
B takes 29 days.
Answer: (B) 29 days
Quantitative Ability · Arithmetic
Time and Work: IPMAT practice questions
24 questions, 3 of them short answer (type the number, as in IPMAT Indore). Each is marked with the exam level it suits. Answer, then open the step-by-step solution.
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A is 100% more efficient than B. B alone can do a job in 24 days. How long will A and B take together?
Solution
A takes 24 ÷ 2 = 12 days alone.
Together: 112 + 124 = 18 per day, so 8 days.
Answer: (C) 8 days
18 workers working 7 hours a day finish a job in 15 days. How many days will 30 workers working 9 hours a day take to finish 3 such jobs?
Solution
Work ∝ workers × days × hours.
Days = 18 × 15 × 7 × 3 / (30 × 9) = 21.
Answer: 21
A and B together finish a job in 18934 days; A alone takes 7 days. How long would B take alone?
Solution
B's rate = 34189 − 17 = 127.
B takes 27 days.
Answer: (A) 27 days
A can do a job in 24 days and B in 24 days. They start together, but A leaves after 6 days. In how many days in all is the job finished?
Solution
In 6 days they finish 6 × (112) = 12 of the job.
B finishes the remaining 12 in 12 days.
Total = 6 + 12 = 18 days.
Answer: (B) 18 days
8 workers working 10 hours a day finish a job in 6 days. How many days will 8 workers working 10 hours a day take to finish 2 such jobs?
Solution
Work ∝ workers × days × hours.
Days = 8 × 6 × 10 × 2 / (8 × 10) = 12.
Answer: (B) 12
Pipes A and B fill a tank in 11 and 4 hours. A leak can empty the full tank in 11 hours. With all three working, how long does the tank take to fill?
Solution
Net rate = 111 + 14 − 111 = 14 of the tank per hour.
Time = 4 hours.
Answer: (D) 4 hours
A can do a job in 19 days and B in 13 days. They start together, but A leaves after 4 days. In how many days in all is the job finished?
Solution
In 4 days they finish 4 × (32247) = 128247 of the job.
B finishes the remaining 119247 in 11919 days.
Total = 4 + 11919 = 19519 days.
Answer: (D) 19519 days
A is 100% more efficient than B. B alone can do a job in 30 days. How long will A and B take together?
Solution
A takes 30 ÷ 2 = 15 days alone.
Together: 115 + 130 = 110 per day, so 10 days.
Answer: (C) 10 days
A and B together finish a job in 17128 days; A alone takes 9 days. How long would B take alone?
Solution
B's rate = 28171 − 19 = 119.
B takes 19 days.
Answer: (C) 19 days
A can do a job in 30 days and B in 8 days. They start together, but A leaves after 3 days. In how many days in all is the job finished?
Solution
In 3 days they finish 3 × (19120) = 1940 of the job.
B finishes the remaining 2140 in 4.2 days.
Total = 3 + 4.2 = 7.2 days.
Answer: (C) 7.2 days
A can do a job in 9 days and B in 11 days. They work on alternate days, A starting first. In how many days is the job finished?
Solution
Take the job as 99 units: A does 11 and B 9 units a day.
Each 2-day pair finishes 20 units. Continue day by day until 99 units are done.
The job is done in 9 89 days.
Answer: (D) 9 89 days
8 workers working 4 hours a day finish a job in 28 days. How many days will 14 workers working 8 hours a day take to finish half the job?
Solution
Work ∝ workers × days × hours.
Days = 8 × 28 × 4 × 12 / (14 × 8) = 4.
Answer: 4
A can do a job in 10 days and B in 7 days. They work on alternate days, A starting first. In how many days is the job finished?
Solution
Take the job as 70 units: A does 7 and B 10 units a day.
Each 2-day pair finishes 17 units. Continue day by day until 70 units are done.
The job is done in 8 27 days.
Answer: (A) 8 27 days
Pipes A and B fill a tank in 4 and 6 hours. A leak can empty the full tank in 24 hours. With all three working, how long does the tank take to fill?
Solution
Net rate = 14 + 16 − 124 = 38 of the tank per hour.
Time = 2 23 hours.
Answer: (B) 2 23 hours
A and B together finish a job in 8.4 days; A alone takes 28 days. How long would B take alone?
Solution
B's rate = 542 − 128 = 112.
B takes 12 days.
Answer: (C) 12 days
A is 25% more efficient than B. B alone can do a job in 30 days. How long will A and B take together?
Solution
A takes 30 ÷ 54 = 24 days alone.
Together: 124 + 130 = 340 per day, so 13 13 days.
Answer: (D) 13 13 days
A can do a job in 6 days and B in 10 days. They work on alternate days, A starting first. In how many days is the job finished?
Solution
Take the job as 30 units: A does 5 and B 3 units a day.
Each 2-day pair finishes 8 units. Continue day by day until 30 units are done.
The job is done in 7 13 days.
Answer: (C) 7 13 days
A can do a job in 28 days and B in 8 days. They start together, but A leaves after 6 days. In how many days in all is the job finished?
Solution
In 6 days they finish 6 × (956) = 2728 of the job.
B finishes the remaining 128 in 27 days.
Total = 6 + 27 = 6 27 days.
Answer: (B) 6 27 days
Pipes A and B fill a tank in 12 and 4 hours. A leak can empty the full tank in 21 hours. With all three working, how long does the tank take to fill?
Solution
Net rate = 112 + 14 − 121 = 27 of the tank per hour.
Time = 3.5 hours.
Answer: (D) 3.5 hours
4 workers working 5 hours a day finish a job in 9 days. How many days will 18 workers working 5 hours a day take to finish the same job?
Solution
Work ∝ workers × days × hours.
Days = 4 × 9 × 5 × 1 / (18 × 5) = 2.
Answer: 2
A is 100% more efficient than B. B alone can do a job in 20 days. How long will A and B take together?
Solution
A takes 20 ÷ 2 = 10 days alone.
Together: 110 + 120 = 320 per day, so 6 23 days.
Answer: (C) 6 23 days
Pipes A and B fill a tank in 12 and 6 hours. A leak can empty the full tank in 14 hours. With all three working, how long does the tank take to fill?
Solution
Net rate = 112 + 16 − 114 = 528 of the tank per hour.
Time = 5.6 hours.
Answer: (D) 5.6 hours
A can do a job in 12 days and B in 8 days. They work on alternate days, A starting first. In how many days is the job finished?
Solution
Take the job as 24 units: A does 2 and B 3 units a day.
Each 2-day pair finishes 5 units. Continue day by day until 24 units are done.
The job is done in 9 23 days.
Answer: (C) 9 23 days
These are original practice questions written by Target Campus in the pattern, syllabus and difficulty of IPMAT Indore, IPMAT Rohtak, JIPMAT, NPAT and SET. They are not previous-year papers.