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Hyderabad: This article is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exam. Here are some practice questions and solutions on the Time and Work topic. 1) A can do a piece of work in 40 days. He worked at it for 5 days and then B finished it […]

Hyderabad: This article is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exam. Here are some practice questions and solutions on the Time and Work topic.
1) A can do a piece of work in 40 days. He worked at it for 5 days and then B finished it in 21 days. They can do it together in ____ days

A. 10 B. 12 C. 14 D. 15

Ans: D

Explanation:

Work done by A in 5 days = 1/40 × 5 = 1/8
Remaining work = (1-1/8) = 7/8

Now remaining work done by B in 21 days
Whole work done by B in 8/7 × 21 = 24 days
A’s 1 day’s work = 1/40 B’s 1 day’s work = 1/24
A B’s 1 day’s work = (1/40 1/24) = 3 5/120 = 8/120 = 1/15

Therefore A B can do a piece of work in 15 days

2) A can do 60% of the work more than B. If B can do it in 24 days. A can do it in ___ days
A. 15 B. 16 C. 17 D. 18
Ans: A
Explanation:
Given that A can do 60% of the work more than B

That means if B can do 100 units of work A can do 160 units of work.

Ratio of work done by A and B = 160:100 = 8:5

Ratio of time taken to finish a work by A and B = 5:8

Therefore 8 = 24 days

In the same way, Then 5 = 15 days

A can do it in 15 days

3) A is twice as good a workman as B. If they finish the work in 14 days, B can do it in ___ days

A. 21 B. 31 C. 39 D. 42

Ans: D

Explanation:

A=2B
Ratio of work done by A and B = 2:1

(A B) 1 day work=1/14

B’s 1 day work = 1/14 × 1/3 = 1/42
Therefore B alone can finish the work in 42 days

4) To do a job B takes three times as long as (A C) can do together. The three men i.e. (A B C) can do a work in 15 days, B alone can do it in ___ days

A. 55 B. 60 C. 65 D. 70

Ans: B

Explanation:

As per given, 3B = (A C)
(A B C) 1 day work=1/15
Sub A C = 3B in above equation

Then, 3B B=1/15

4B = 1/15 =>; B=1/60 (1 day work)

So, B alone can do work in 60 days

5) A, B and C can do a piece of work in 24, 40 and 30 days viz., They began the work together but B left 4 days before the completion of work. The work was done in ____ days

A. 12 B. 7 C. 11 D. 18

Ans: C

Explanation:

Last 4 days work done by A and C only
4 days work of A and C = 4 (1/24 1/30)=4((5 4)/120) = 3/10
Remaining Work = 1 – 3/10 = 7/10

(A B C) 1 day work = 1/24 1/40 1/30
Then, (A B C) 1 day work = 5 3 4/120 = 12/120 = 1/10

1 day work of A, B and C is = 1/10

7 days work of A, B and C is = 7 × 1/10 = 7/10
Therefore they can complete the work in 7 4 = 11 days

6) A is three times as fast as B and together they can finish the work in 12 days. A alone can do it in ___ days

16 B. 17 C. 18 D.19

Ans: A
Explanation:
Given, A is three times as fast as B; A= 3B

Ratio of work done by A and B = 3:1
Ratio of time taken to finish a work by A and B = 1:3

Assume that can finish the work in x days

A & B together work per a day is, A B= 1/12

1/x 1/3x = 1/12

1 3/3x = 1/12
3x = 48 =>; x = 16