Practice questions for time and work problems
This is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exam. Here are some practice questions and explanations on the Time and Work topic. To improve calculation speed, the aspirants must practice questions from the previous question papers. 1. Twenty women can do a work in 16 days. Sixteen […]
This is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exam. Here are some practice questions and explanations on the Time and Work topic. To improve calculation speed, the aspirants must practice questions from the previous question papers.
1. Twenty women can do a work in 16 days. Sixteen men can complete the same work in 15 days. What is the ratio between the capacity of a man and a woman?
A. 3:4
B. 4:3
C. 5:3
D. 5:9
Ans: B
Explanation:
(20 x 16) women can complete the work in 1 day.
1 woman’s 1 day’s work = 1/320 .
(16 x 15) men can complete the work in 1 day.
1 man’s 1 day’s work = 1/240
So, required ratio = 1/240 : 1/320
= 4: 3 (cross multiplied)
2. A does 1/3 of the work in 5 days. He is then assisted by B and they together finish the remaining work in 6 days. B alone can do it in ____ days
A. 22
B. 22.25
C. 22.50
D. 23.50
Ans: C
Explanation:
Work done by A in 5 days = 1/5
Work done by A in 1 day = ((1/3)/5) = 1/15
Work done by A and B in 6 days = 2/3 [since 1- 1/3 = 2/3]
Work done by A and B in 1 day = (2/3)/6
= 2/18 =>; 1/9
Work done by B in 1 day = 1/9 – 1/15
= 5-3/45 ; [LCM of 9,15 is 45] = 2/45
B can complete the work 45/2 in days = 22.5 days
3. 2 men and 3 boys can do a work in 8 days and 3 men and 2 boys in 7 days. 5 men and 4 boys will do it in ___ days.
A. 1
B. 2
C. 3
D. 4
Ans: D
Explanation:
Let 1 man’s 1 day’s work = x and 1 boy’s 1 day’s work = y.
Then 2x 3y= 1/8
3x 2y= 1/7
By solving, x=1/28 and y=1/56
Work done by 5 men and 4 women in 1 day = 5/28 4/56
= (10 4)/56 =>; 14/56
Time taken by 5 men and 4 women in doing the work= 56/14 = 4 days
4. A and B can do a piece of work in 25 days. After A worked for 20 days, B finished the remaining work in 30 days. A alone can do it in_____ days.
A. 50
B. 90
C. 80
D. 70
Ans: A
Explanation:
A and B can do a piece of work in 25 days
A and B can work in a day is, A B=1/25
A worked for 20 days and B completed the remaining work in 30 days
Now, total work done in 20 days by both of them = (1/25)×20=4/5
Remaining work = 1× (4/5) = 1/5
This work was completed by B alone in 10 days.
Therefore, days taken by B to complete a unit of work = 10÷(1/5) =50 days
Work done by A in 1 day = 1/25 – 1/50 = (2-1)/50=1/50
Hence, A can complete the work in 50 days
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