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Time and Work - Aptitude Questions and Answers - RejinpaulPlacement

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15.
A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together , they will complete the same work in: [C.B.I. 2003]
Answer & Solution
Answer: c) 3    3/7 days

Solution:   (A + B + C)'s 1 day's work = (1/24 + 1/6 + 1/12) = 7/24

So, A, B and C together will complete the job in 24/7 = 3    3/7 days.
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16.
A man can do a job in 15 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together? [Hotel Management 2003]
Answer & Solution
Answer: c) Approximately 6.4 days

Solution:   1 day's work of the three persons = (1/15 + 1/20 + 1/25) = 47/300

So , all the three together will complete the work in 300/47 ~ 6.4 days
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17.
A man can do a piece of work in 5 days, but with the help of his son, he can do it in 3 days. In what time can the son do it alone? [S.S.C 2004]
Answer & Solution
Answer: c) 7    1/2 days

Solution:   Son's 1 day's work = (1/3 - 1/5) = 2/15

The son alone can do the work in 15/2 = 7   1/2 days
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18.
A can lay railway tracks between two given stations in 16 days and B can do the same job in 12 days. With the help of C, they did the job in 4 days only. Then , C alone can do the job in: [S.S.C 2003]
Answer & Solution
Answer: c) 9   3/5 days

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

A's 1 day's work = 1/16
B's 1 day's work = 1/12
C's 1 day's work = 1/4 - (1/16 + 1/12) = (1/4 - 7/48) = 5/48

So, C alone can do the work in 48/5 = 9   3/5 days
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19.
A takes twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in: [S.S.C. 2002]
Answer & Solution
Answer: b) 6 days

Solution:   Suppose A, B and C take x, x/2 and x/3 hours respectively to finish the work.

Then, (1/x + 2/x + 3/x) = 1/2
=> 6/x = 1/2
=> x = 12.

So, B takes 6 hours to finish the work.
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20.
X can do 1/4 of a work in 10 days, Y can do 40% of the work in 40 days and Z can do 1/3 of the work in 13 days. Who will complete the work first?
Answer & Solution
Answer: c) Z

Solution:   Whole work will be done by X in (10 * 4) = 40 days
Whole work will be done by Y in [40 * (100/40)] = 100 days.
Whole work will be done by Z in (13 * 3) = 39 days

Z will complete the work first.
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21.
P, Q and R are three typists who working simultaneously can type 216 pages in 4 hours. In one hour, R can type as many pages more than Q as Q can type more than P. During a period of five hours, R can type as many pages as P can during seven hours. How many pages does each of them type per hour?
Answer & Solution
Answer: c) 15, 18, 21

Solution:   Let the number of pages typed in one hour by P, Q and R be x, y and z respectively.

Then,
x + y + z = 216/4
=> x + y + z = 54 ....(i)
z - y = y - x
=> 2y = x + z ..... (ii)
5z = 7x
=> x = (5/7)x ...... (iii)

Solving (i), (ii), and (iii), we get x = 15, y = 18, z = 21
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