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Time and Work - Aptitude Questions and Answers - RejinpaulPlacement

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43.
X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last? [Bank P.O. 2004]
Answer & Solution
Answer: b) 10 days

Solution:   Work done by X in 4 days = [(1/20) * 4] = 1/5.
Remaining work = [1 - (1/5)] = 4/5

(X + Y)'s 1 day's work = [1/20 + 1/12] = 8/60 = 2/15.

Now, 2/15 work is done by X and Y in 1 day.
So, 4/5 work will be done by X and Y in [(15/2) * (4/5)] = 6 days.

Hence, total time taken = (6 + 4) days = 10 days.
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44.
A and B can together finish a work in 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days, A alone can finish the job? [S.S.C. 2003]
Answer & Solution
Answer: d) 60

Solution:   (A + B)'s 29 day's work = [(1/30) * 20] = 2/3.
Remaining work = [1 - (2/3)] = 1/3.

Now, 1/3 work is done by A in 20 days.

Whole work will be done by A in (20 * 3) = 60 days.
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45.
X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work? [Hotel Management 1999]
Answer & Solution
Answer: b) 13   1/3 days

Solution:   Work done by X in 8 days = [1/40) * 8] = 1/5.
Remaining work = [1 - (1/5)] = 4/5.

Now, 4/5 work is done by Y in 16 days.
Whole work will be done by Y in [16 * (5/4)] = 20 days.

X's 1 day's work = 1/40
Y's 1 day's work = 1/20

(X + Y)'s 1 day's work = [1/40 + 1/20] = 3/40.

Hence, X and Y will together complete the work in 40/3 = 13   1/3 days.
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46.
A, B and C together can complete a piece of work in 10 days. All the three started working at it together and after 4 days A left. Then B and C together completed the work in 10 more days. A alone could complete the work in:
Answer & Solution
Answer: c) 25 days

Solution:   Work done by A, B and C in 4 days = [(1/10) * 4] = 2/5.
Remaining work = [1 - (2/5)] = 3/5

Now, 3/5 work is done by B and C in 10 days.
Whole work will be done by B and C in [10 * 5/3] = 50/3 days.

(A + B + C)'s 1 day's work = 1/10
(B + C)'s 1 day's work = 3/50

A's 1 day's work = [1/10) - (3/50)] = 2/50 = 1/25.

A alone could complete the work in 25 days.
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47.
A does 4/5 of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work? [S.S.C 2002]
Answer & Solution
Answer: c) 37   1/2 days

Solution:   Whole work is done by A in [20 * (5/4)] = 25 days.
Now, [1 - (4/5)] i.e., 1/5 work is done by A and B in 3 days.

Whole work will be done by A and B in (3 * 5) = 15 days.

A's 1 day's work = 1/25.
(A + B)'s 1 day's work = 1/15.
B's 1 day's work = [1/15 - 1/25] = 4/150 = 2/75.

So, B alone would do the work in 75/2 = 37   1/2 days.
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48.
A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone? [C.B.I. 1997]
Answer & Solution
Answer: c) 60 days

Solution:   Let A's 1 day's work = x and B's 1 day's work = y.
Then x + y = 1/30 and 16x + 44y = 1.

Solving these two equations, we get : x = 1/60 and y = 1/60.

B's 1 day's work = 1/60

Hence, B alone shall finish the whole work in 60 days.
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49.
A and B together can do a piece of work in 12 days, which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C finishes it in 13 days. In how many days C alone will do the work?
Answer & Solution
Answer: b) 24 days

Solution:   A's 5 day's work + B's 7 day's work + C's 13 day's work = 1

=> (A + B)'s 5 day's work + (B + C)'s 2 day's work + C's 11 day's work = 1

=> 5/12 + 2/16 + C's 11 day's work = 1

=> C's 11 day's work = 1 - (5/12 + 2/16) = 11/24

=> C's 1 day's work = [(11/24) * (1/11)] = 1/24

C alone can finish the work in 24 days.
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