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Time and Work - Aptitude Questions and Answers - RejinpaulPlacement

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36.
Two workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1/3 as efficiently as he actually did, the work would have been completed in 3 days. A alone could complete the work in:
Answer & Solution
Answer: b) 6   1/4 days

Solution:   Let A's 1 day's work = x and B's 1 day's work = y.
Then, x + y = 1/5 and 2x + 1/3 y = 1/3.

Solving, we get: x = 4/25 and y = 1/25.

A's 1 day's work = 4/25

So, A alone could complete the work in 25/4 = 6   1/4 days.
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37.
A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is: [S.S.C. 2000]
Answer & Solution
Answer: d) 8/15

Solution:   A's 1 day 's work = 1/15
B's 1 day's work = 1/20

(A + B)'s 1 day's work = [(1/15) + (1/20)] = 7/60
(A + B)'s 4 day's work = [(7/60) * 4] = 7/15

Remaining work = [1 - (7/15)] = 8/15
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38.
A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left job. In how many days, A alone can finish the remaining work? [Bank P.O. 2002]
Answer & Solution
Answer: c) 6

Solution:   B's 10 day's work = [(1/15) * 10] = 2/3
Remaining work = [1 - (2/3)] = 1/3

Now, 1/18 work is work by A in 1 day.

1/3 work is done by A in [18 * (1/3)] = 6 days.
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39.
A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in: [S.S.C. 2004]
Answer & Solution
Answer: c) 12 days

Solution:   (A + B)'s 1 day's work = (1/15 + 1/10) = 1/6

Work done by A and B in 2 days = [(1/6) * 2] = 1/3.
Remaining work = [1 - (1/3)] = 2/3

Now 1/15 work is done by A in 1 day.
2/3 work will be done by A in[15 * (2/3)] = 10 days.

Hence total time taken = 10 + 2 = 12 days.
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40.
A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in: [S.S.C 2003]
Answer & Solution
Answer: c) 10 days

Solution:   (B + C)'s 1 day's work = (1/9 + 1/12) = 7/36

Work done by B and C in 3 days = [(7/36) * 3] = 7/12
Remaining work = [1 - (7/12)] = 5/12

Now, 1/24 work is done by A in 1 day.

So, 5/12 work is done by A in [24 * (5/12)] = 10 days.
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41.
A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 a.m. while machine P is closed at 11 a.m. and the remaining two machines complete the work. Approximately at what time will the work be finished? [Bank P.O. 2003]
Answer & Solution
Answer: d) 1 p.m.

Solution:   (P + Q + R)'s 1 hour's work = [1/8 + 1/10 + 1/12] = 37/120

Work done by P, Q and R in 2 hours = [(37/120) * 2] = 37/60
Remaining work = [1 - (37/60)] = 23/60.

(Q + R)'s 1 hour's work = [1/10 + 1/12] = 11/60.

Now, 11/60 work is done by Q and R in 1 hour.
So, 23/60 work will be done by Q and R in[(60/11) * (23/60)] = 23/11 hours = 2 hours.

So, the work will be finished approximately 2 hours after 11 a.m., i.e. around 1 p.m.
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42.
A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work? [C.B.I. 2003]
Answer & Solution
Answer: d) 18 days
Solution:   2 (A + B + C)'s 1 day's work = [1/30 + 1/24 + 1/20] = 15/120 = 1/8
=> (A + B + C)'s 1 day's work = 1/16.

Work done by A, B abd C in 10 days = 10/16 = 5/8
Remaining work = [1 - (5/8)] = 3/8

A's 1 day's work = [(1/16) - (1/24)] = 1/48
Now, 1/48 work is done by A in 1 day.

So, 3/8 work will be done by A in [48 * (3/8)] = 18 days
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