PlacementPrepA can finish a job in 18 days and B in 6 days. In how many days can they finish it working together?
Solution
In one day they do 1/18 + 1/6 = 2/9 of the job.
Time = 1 ÷ 2/9 = 4.5 days.
Answer: (C) 4.5 days
Quantitative Aptitude · Work and motion
Time and Work: placement practice questions
30 moderate questions in the pattern of campus placement tests. Pick an option to check your answer, then open the step-by-step solution.
A and B together finish a work in 8 days. A alone takes 10 days. How long will B alone take?
Solution
B's one-day work = 1/8 − 1/10 = 1/40.
So B takes 40 days.
Answer: (D) 40 days
A can do a work in 30 days and B in 10 days. They work together for 2 days, then A leaves. In how many days in all is the work finished?
Solution
In 2 days together they finish 2 × (2/15) = 4/15.
Remaining 11/15 is done by B in 11/15 × 10 = 7 1/3 days.
Total = 2 + 7 1/3 = 9 1/3 days.
Answer: (D) 9 1/3 days
10 men can finish a job in 12 days. How many days will 6 men take to finish the same job?
Solution
Total work = 10 × 12 = 120 man-days.
Days = 120 ÷ 6 = 20.
Answer: (A) 20 days
A is 2 times as efficient as B. Together they finish a work in 24 days. How long would A alone take?
Solution
If B takes x days, A takes x/2 days. Together: 3/x per day.
x/3 = 24 gives x = 72, so A takes 36 days.
Answer: (B) 36 days
A can do a work in 15 days and B in 12 days. They earn Rs. 3600 together for the work. What is A's share?
Solution
Shares are in the ratio of work done per day: 1/15 : 1/12 = 12 : 15.
A's share = 12/27 × 3600 = 1600.
Answer: (D) Rs. 1600
A and B together finish a work in 180/17 days. A alone takes 15 days. How long will B alone take?
Solution
B's one-day work = 1/180/17 − 1/15 = 1/36.
So B takes 36 days.
Answer: (D) 36 days
A can do a work in 20 days and B in 10 days. They work together for 5 days, then A leaves. In how many days in all is the work finished?
Solution
In 5 days together they finish 5 × (0.15) = 0.75.
Remaining 0.25 is done by B in 0.25 × 10 = 2.5 days.
Total = 5 + 2.5 = 7.5 days.
Answer: (C) 7.5 days
24 men can finish a job in 12 days. How many days will 9 men take to finish the same job?
Solution
Total work = 24 × 12 = 288 man-days.
Days = 288 ÷ 9 = 32.
Answer: (C) 32 days
A is 3 times as efficient as B. Together they finish a work in 11.25 days. How long would A alone take?
Solution
If B takes x days, A takes x/3 days. Together: 4/x per day.
x/4 = 11.25 gives x = 45, so A takes 15 days.
Answer: (B) 15 days
A can finish a job in 24 days and B in 30 days. In how many days can they finish it working together?
Solution
In one day they do 1/24 + 1/30 = 3/40 of the job.
Time = 1 ÷ 3/40 = 13 1/3 days.
Answer: (A) 13 1/3 days
A and B together finish a work in 10 days. A alone takes 12 days. How long will B alone take?
Solution
B's one-day work = 1/10 − 1/12 = 1/60.
So B takes 60 days.
Answer: (A) 60 days
A can do a work in 15 days and B in 10 days. They work together for 3 days, then A leaves. In how many days in all is the work finished?
Solution
In 3 days together they finish 3 × (1/6) = 0.5.
Remaining 0.5 is done by B in 0.5 × 10 = 5 days.
Total = 3 + 5 = 8 days.
Answer: (D) 8 days
A is 2 times as efficient as B. Together they finish a work in 12 days. How long would A alone take?
Solution
If B takes x days, A takes x/2 days. Together: 3/x per day.
x/3 = 12 gives x = 36, so A takes 18 days.
Answer: (B) 18 days
A and B together finish a work in 16 4/11 days. A alone takes 30 days. How long will B alone take?
Solution
B's one-day work = 1/16 4/11 − 1/30 = 1/36.
So B takes 36 days.
Answer: (C) 36 days
A is 2 times as efficient as B. Together they finish a work in 16 days. How long would A alone take?
Solution
If B takes x days, A takes x/2 days. Together: 3/x per day.
x/3 = 16 gives x = 48, so A takes 24 days.
Answer: (A) 24 days
A and B together finish a work in 6 days. A alone takes 10 days. How long will B alone take?
Solution
B's one-day work = 1/6 − 1/10 = 1/15.
So B takes 15 days.
Answer: (A) 15 days
A can do a work in 10 days and B in 20 days. They work together for 3 days, then A leaves. In how many days in all is the work finished?
Solution
In 3 days together they finish 3 × (0.15) = 0.45.
Remaining 0.55 is done by B in 0.55 × 20 = 11 days.
Total = 3 + 11 = 14 days.
Answer: (B) 14 days
24 men can finish a job in 20 days. How many days will 8 men take to finish the same job?
Solution
Total work = 24 × 20 = 480 man-days.
Days = 480 ÷ 8 = 60.
Answer: (C) 60 days
A can do a work in 12 days and B in 15 days. They earn Rs. 3600 together for the work. What is A's share?
Solution
Shares are in the ratio of work done per day: 1/12 : 1/15 = 15 : 12.
A's share = 15/27 × 3600 = 2000.
Answer: (C) Rs. 2000
A can do a work in 15 days and B in 12 days. They work together for 5 days, then A leaves. In how many days in all is the work finished?
Solution
In 5 days together they finish 5 × (0.15) = 0.75.
Remaining 0.25 is done by B in 0.25 × 12 = 3 days.
Total = 5 + 3 = 8 days.
Answer: (B) 8 days
A is 3 times as efficient as B. Together they finish a work in 18 days. How long would A alone take?
Solution
If B takes x days, A takes x/3 days. Together: 4/x per day.
x/4 = 18 gives x = 72, so A takes 24 days.
Answer: (C) 24 days
A can do a work in 8 days and B in 12 days. They earn Rs. 1800 together for the work. What is A's share?
Solution
Shares are in the ratio of work done per day: 1/8 : 1/12 = 12 : 8.
A's share = 12/20 × 1800 = 1080.
Answer: (C) Rs. 1080
A and B together finish a work in 8 4/7 days. A alone takes 15 days. How long will B alone take?
Solution
B's one-day work = 1/8 4/7 − 1/15 = 0.05.
So B takes 20 days.
Answer: (A) 20 days
A can do a work in 10 days and B in 30 days. They work together for 5 days, then A leaves. In how many days in all is the work finished?
Solution
In 5 days together they finish 5 × (2/15) = 2/3.
Remaining 1/3 is done by B in 1/3 × 30 = 10 days.
Total = 5 + 10 = 15 days.
Answer: (D) 15 days
A can do a work in 12 days and B in 6 days. They earn Rs. 4500 together for the work. What is A's share?
Solution
Shares are in the ratio of work done per day: 1/12 : 1/6 = 6 : 12.
A's share = 6/18 × 4500 = 1500.
Answer: (A) Rs. 1500
12 men can finish a job in 18 days. How many days will 9 men take to finish the same job?
Solution
Total work = 12 × 18 = 216 man-days.
Days = 216 ÷ 9 = 24.
Answer: (B) 24 days
A is 3 times as efficient as B. Together they finish a work in 9 days. How long would A alone take?
Solution
If B takes x days, A takes x/3 days. Together: 4/x per day.
x/4 = 9 gives x = 36, so A takes 12 days.
Answer: (D) 12 days
A can do a work in 12 days and B in 15 days. They earn Rs. 1800 together for the work. What is A's share?
Solution
Shares are in the ratio of work done per day: 1/12 : 1/15 = 15 : 12.
A's share = 15/27 × 1800 = 1000.
Answer: (D) Rs. 1000
A can finish a job in 18 days and B in 30 days. In how many days can they finish it working together?
Solution
In one day they do 1/18 + 1/30 = 4/45 of the job.
Time = 1 ÷ 4/45 = 11.25 days.
Answer: (D) 11.25 days
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