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Time and Work - Aptitude Questions and Answers - RejinpaulPlacement

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22.
Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages? [SCMHRD 2002]
Answer & Solution
Answer: c) 8 hours 15 minutes

Solution:   Number of pages typed by Ronald in 1 hour = 32/6 = 16/3
Number of pages typed by Elan in 1 hour = 40/5 = 8.

Number of pages typed by both in 1 hour = [(16/3 + 8) = 40/3.

Time taken by both to type 110 pages = [110 * (3/40)] hrs = 8   1/4 hrs = 8 hrs 15 minutes.
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23.
P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work? [Bank P.O. 1999]
Answer & Solution
Answer: b) 5 5/11

Solution:   P can complete the work in (12 * 8) hrs. = 96 hrs.
Q can complete the work in (8 * 10) hrs. = 80 hrs.

P's 1 hour's work = 1/96 and Q's 1 hour's work = 1/80
(P + Q)'s 1 hour's work = [(1/96) + (1/80)] = 11/480

So, both P and Q will finish the work in (480/11) hrs.

Number of days of 8 hours each = [(480/11) * (1/8)] = 60/11 days = 5 5/11 days.
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24.
A and B can do a work in 12 days, B and C in 15 days, C and A in 20 days. If A, B and C work together, they will complete the work in: [S.S.C 1999]
Answer & Solution
Answer: c) 10 days

Solution:   (A + B)'s 1 day's work = 1/12
(B + C)'s 1 day's work = 1/15
(A + C)'s 1 day's work = 1/20

Adding, we get, 2(A + B + C)'s 1 day's work = [(1/12) + (1/15) + (1/20)] = 12/60 = 1/5
(A + B + C)'s 1 day's work = 1/10

So, A, B abd C together can complete the work in 10 days.
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25.
A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in: [R.R.B. 2001]
Answer & Solution
Answer: c) 8 days

Solution:   (A + B + C)'s 1 day's work = 1/6
(A + B)'s 1 day's work = 1/8
(B + C)'s 1 day's work = 1/12

(A + C)'s 1 day's work = [2 * (1/6)] - [(1/8) + (1/12)] [(1/3) - (5/24)] = 3/24 = 1/8

So, A and C together will do the work in 8 days.
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26.
A and B can do a piece of work in 72 days, B and C can do it in 120 days, A and C can do it in 90 days. In what time can A alone do it?
Answer & Solution
Answer: c) 120 days

Solution:   (A + B)'s 1 day's work = 1/72
(B + C)'s 1 day's work = 1/120
(A + C)'s 1 day's work = 1/90

Adding, we get: 2 (A + B + C)'s 1 day's work = (1/72 + 1/120 + 1/90) = 12/360 = 1/30
=> (A + B + C)'s 1 day's work = 1/60

So, A's 1 day's work = (1/60 - 1/120) = 1/120

A alone can do the work in 120 days.
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27.
A and B can do a piece of work in 5 days, B and C can do it in 7 days, A and C can do it in 4 days. Who among these will take the least time if put to do it alone?
Answer & Solution
Answer: c) A

Solution:   (A + B)'s 1 day's work = 1/5
(B + C)'s 1 day's work = 1/7
(A + C)'s 1 day's work = 1/4

Adding, we get: 2 (A + B + C)'s 1 day's work = (1/5 + 1/7 + 1/4) = 83/140
=> (A + B + C)'s 1 day's work = 83/280

A's 1 day's work = [(83/280) - (1/7)] = 43/280
B's 1 day's work = [(83/280) - (1/4)] = 13/280
C's 1 day's work = [(83/280) - (1/5)] = 27/280

Thus time taken by A, B, C is 280/43 days, 280/13 days, 280/27 days respectively.

Clearly, the time taken by A is least
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28.
A can do a piece of work in 4 hours, B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it? [S.S.C. 2002]
Answer & Solution
Answer: c) 12 hours

Solution:   A's 1 hour's work = 1/4
(B + C)'s 1 hour's work = 1/3
(A + C)'s 1 hour's work = 1/2

(A + B + C)'s 1 hour's work = (1/4 + 1/3) = 7/12

B's 1 hour's work = (7/12 - 1/2) = 1/12

B alone will take 12 hours to do the work
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