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# Arithmetic Aptitude :: Time and Work

Home > Arithmetic Aptitude > Time and Work > General Questions

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21. A can lay railway track 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 :

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Explanation:

1 day's work done by A = 1/16
1 day's work done by B = 1/12
1 day's work done by (A, B and C) = 1/4
=> so C 1 day's work = (1/4-1/12-1/16) = (12/48-4/48-3/48) = 5/48
so C alone can do the work = 48/5 days = 9 3/5 days

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22. 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 .

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Explanation:

Let's suppose A, B and C take x, x/2 and x/3 hours respectively to finish the work.

So their 1 day's work (1/x+2/x+3/x)=1/2 => 6/x = 1/2
=> x=12

So, B take 6) hours to finish the work.

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23. 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. if 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 ?

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Explanation:

find the (P + Q + R)'s 1 hour's work = (1/8+1/10+1/12) = 37/120

So Work done by P, Q and R in 2 hours = (2*37/120) = 37/60

Now find the Remaining work = (1?37/60) = 23/60

(Q + R)'s 1 hour's work = (1/10+1/12) = 11/60
OR
Time taken to do 11/60 part of work by (Q+R) = 1 hrs.
=> so to do whole work by (Q&R) = 60/11 hrs
so for 23/60 part of work = (23/60*60/11) hrs. = 23/11 = ~2 hrs.

So, the work will be finished approximately 2 hours after 11 a.m . i.e., around 1 p.m.

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24. 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:

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Explanation:

(A+ B)'s 1 day's work = (1/15+1/10) = 5/30 = 1/6

So work done by A and B in 2 days = (1/6?2) = 1/3

so Remaining work = (1?1/3) = 2/3

A 1 day work = 1/15
or
1/15 work is done by A in = 1 day.

? 2/3 work will be done by A = (15?2/3) = 10 days.

so total time required = (10 + 2) = 12 days.

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25. 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 :

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Explanation:

A's 1 day work = 1/24
B's 1 day work = 1/9
C's 1 day work = 1/12

S0 (B + C)'s 1 day's work = (1/9+1/12)=7/36

Work done by B and C in 3 days = (3*7/36)=7/12

left work = (1?7/12)=5/12

.

1/24 part of work done by A = 1 day.

So 5/12 part of work is done by A = (24?5/12) = 10 days.

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26. P can do a piece of work in 40 days. He works at it for 8 days arid then Q finished it in 16 days. How long will they together take to complete the work ?

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Explanation:

P one day work = 1/40
So P 8 days Work = (8*1/40)=1/5

Left work = (1?1/5)=4/5

4/5 part of work is done by Q = 16 days.

So Whole work will be done by Q = [16/(4/5)] = 16*5/4 = 20 days.

Q's 1 day's work = 1/20

(P + Q)'s 1 day's work = (1/40+1/20) = 3/40

Hence,( P and Q) together complete the work = 40/3=13 1/3 days.

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27. 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 ?

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Explanation:

4/5 part of work done by A = 20 days.

Whole work is done by A = (20?5/4) = 25 days.

Left work = (1-4/5) = 1/5

1/5 part of work is done by (A & B) = 3 days.

Whole work will be none by A and B = (3 x 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)=10/(15*25)=2/75

So, B alone would do the work in 75/2=37 1/2 days.

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28. 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 :

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Explanation:

(A,B and C) 1 day work = 1/10
Work done by (A, B and C) in 4 days = 4*1/10=2/5
Left work = (1?2/5)=3/5

3/5 part of work is done by (B and C) = 10 days.

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

So Whole work will be done by (B and C) = (10?5/)3 = 50/3 days.
=> (B+C)'s 1 day work = 3/50
A's 1 day's work = (1/10?3/50)=2/50=1/25

So A alone could complete the work in 25 days.

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29. 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 ?

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Explanation:

1 day's work done by man = 1/5
1 day's work done by man and his son = 1/3
=> His son 1 day's work = (1/3-1/5) = (5/15-3/15) = 2/15
so his son can do it alone = 15/2 days = 7 1/2 days

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30. A and B can finish a piece of work in 20 days .B and C in 30 days and C and A in 40 days. In how many days will A alone finish the job

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Explanation:

Find one day work for all three
(A+B)'s 1 day work = 1/20 ----(1)
(B+C)'s 1 day work = 1/30 ----(2)
and (C+A)'s 1 day work = 1/40 ----(3)
2(A+B+C) 1 day work = (1/20 + 1/30 + 1/40)
=> (A+B+C) = (6+4+3)/2*120
=> (A+B+C) = 13/240 -----------(4)
By eq. (2) and (4)
A + 1/30 = 13/240
=> A = 13/240 - 1/30 = (13-8)/240 = 1/48
then A's 1 day work = 1/48
so A alon can finish the job = 48 days

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