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Time and Work - Aptitude Questions and Answers - RejinpaulPlacement

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29.
A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in: [S.S.C 2003]
Answer & Solution
Answer: c) 25 days

Solution:   (A + B)'s 1 day's work = 1/10
C's 1 day's work = 1/50

(A + B + C)'s 1 day's work = (1/10 + 1/50) = 6/50 = 3/25 ....... (i)
Also, A's 1 day's work = (B + C)'s 1 day's work .......(ii)

From (i) and (ii), we get : 2 * (A's 1 day's work) = 3/25
=> A's 1 day's work = 3/50
B's 1 day's work = (1/10 - 3/50) = 2/50 = 1/25

So, B alone could do the work in 25 days.
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30.
A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work is: [Asstt. Grade. 1997]
Answer & Solution
Answer: d) 4 days

Solution:   Ratio of rates of working of A and B = 2 : 1.
So, ratio of time taken = 1 : 2.

A's 1 day's work = 1/6
B's 1 day's work = 1/12

(A + B)'s 1 day's work = (1/6 + 1/12) = 3/12 = 1/4

So, A and B together can finish the work in 4 days
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31.
A is thrice as good a workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in: [S.S.C. 1999]
Answer & Solution
Answer: b) 22   1/2 days

Solution:   Ratio of times taken by A and B = 1 : 3.

If difference of time is 2 days, B takes 3 days.
If difference of time is 60 days, B takes [(3/2) * 60] = 90 days.

So, A takes 30 days to do the work.

A's 1 day's work = 1/30
B's 1 day's work = 1/90
(A + B)'s 1 day's work = (1/30 + 1/90) = 4/90 = 2/45

A and B together can do the work in 45/2 = 22   1/2 days.
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32.
A and B can do a job together in 7 days. A is 1   3/4 times as efficient as B. The same job can be done by A alone in: [S.S.C. 2003]
Answer & Solution
Answer: b) 11 days

Solution:   (A's 1 day's work) : (B's 1 day's work) = 7/4 : 1 = 7 : 4.

Let A's and B's 1 day's work be 7x and 4x respectively.
Then, 7x + 4x = 1/7
11x = 1/7
x = 1/77

A's 1 day's work = [(1/77) * 7] = 1/11

So, A alone can the job in 11 days.
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33.
A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days? [Hotel Management 1998]
Answer & Solution
Answer: b) 13 days

Solution:   Ratio of time taken by A and B = 100 : 130 = 10 : 13.

Suppose B takes x days to do the work.
Then, 10 : 13 :: 23 : x
=> x = [(23 * 13) /10]
=> x = 299/10

A's 1 day's work = 1/23
B's 1 day's workk = 10/299

(A + B)'s 1 day's work = [(1/23) + (10/299)] = 23/299 = 1/13

A and B together can complete the job in 13 days.
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34.
A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it?
Answer & Solution
Answer: c) 30 days

Solution:   Suppose B takes x day to do the work.

A takes [2 * (3/4)x] = 3x/2 days to do it.

(A + B)'s 1 day's work = 1/18

1/x + 2/3x = 1/18 or x = 30.
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35.
A is 50% as efficient as B. C does half of the work done by A and B together. If C alone does the work in 40 days, then A, B and C together can do the work in:
Answer & Solution
Answer: d) 13    1/3 days

Solution:   (A's 1 day's work) : (B's 1 day's work) = 150 : 100 = 3 : 2.

Let A's and B's 1 day's work be 3x and 2x respectively.

Then, C's 1 day's work = [(3x + 2x)/2] = 5x/2

5x/2 = 1/40 or x = [(1/40) * (2/5)] = 1/100

A's 1 day's work = 3/100
B's 1 day's work = 1/50
C's 1 day's work = 1/40

(A + B + C)'s 1 day's work = [(3/100) + (1/50) + (1/40)] = 15/200 = 3/40

So, A, B and C together can do the work in 40/3 = 13    1/3 days
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