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# Arithmetic Aptitude :: Time and Work

Home > Arithmetic Aptitude > Time and Work > General Questions

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61. A can do a certain work in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same job?

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Explanation:

A=100% work one day(1 work)
B=160% work one day(1.6 work)

So 12/1.6 = 7.5 days.

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62. One man, 3 women and 4 boys can do a piece of work in 96 hours, 2 men and 8 boys can do it in 80 hours, 2 men & 3 women can do it in 120 hours. 5 Men & 12 boys can do it in how many hours?

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Explanation:

Lets assume man, women and boy as M, W, B respectively.
So, m+3W+4B=1/96 ------- (1)
2M+8B=1/80 -------- (2)
2M+3W=1/120 ---------(3)
By solving above eq.
4M+16B=1/40 4
eq(3)+eq(4)
5M+12B+(M+3W+4B) = 1/40+1/120
5M+12B=11/480 = 43 7/11 hrs.

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63. A does 4/5 of 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:

A can do 4/5th works in 20 days.
so he can do the whole work in 20*(5/4) =25 days.
remaining work after done 4/5 by A is=1-(4/5)=1/5
(A+B) can do the 1/5th work in 3 days.
means the can do the whole work in (3*5)=15 days.
so,(A+B)'s 1 days work=1/15
B's 1 day's work {(1/15)-(1/25)}=2/75
so B can alone do the whole work in 75/2,means in 37 1/2 days.

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64. 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1. boy do the work? .

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Explanation:

If 1 day work of a man=m and a boy=b, then
2m + 3b =1/10 ----(i) and
3m + 2b =1/8 ----(ii)
On solving (i) and (ii), m=7/200, b=1/100
So 2 men and 1 boy's 1 day work= (2*7/200)+(1/100)=8/100=2/25
Hence they can complete the work in 25/2=12.5 days

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65. A and B undertake to do a piece of work for Rs. 600. A alone can- do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of each.

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Explanation:

C's 1 day's work=1/3 - (1/6 + 1/8)
A:B:C = Ratio of their 1 day's work = 1/6 : 1/8 : 1/24= 4:3:1 (by taking LCM)
therefore,
A's Share = Rs.(600* 4/8) = Rs.300
B's Share = Rs.(600* 3/8) = Rs.225
C's Share = Rs.[600 - (300 + 225)] = Rs.75

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66. A is 6 times as fast as B and takes 100 days less to complete a work than B. find the total no of days taken by A and B to complete the work.

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Explanation:

Given, A is 6 times as fast as B
So, Ratio of time taken by A and B will be 1:6
Lets assume time taken by A = x.
and time taken by B = 6x.
According to the question, A take 100 days less.
=> 6x-x=100 .
=> x=20.
So, A takes 20 days and B takes 120 days to complete the work.
A's 1 day work = 1/20.
B's 1 day work = 1/120.
(A+B)'s 1 day work = 1/20 + 1/120 = 7/120.
Therefor, total time taken by A & B = 120/7 days.

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67. A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternatively, A beginning, in how many days, the work will be completed?

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Explanation:

(A+B)'s 2 days work = (1/9 + 1/12)= 7/36
(A+B)'s 10 days work = 10/2 *7/36 = 35/36
So, remaining work (1- 35/36) = 1/36
its done by A in 9* 1/36 = 1/4 day
Total time = 10 +1/4 = 41/4 days.

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68. Sixteen men complete a work in 24 days while 48 children can do it in 16 days. Twelve men started the work, after 14 days 12 children joined them. In how Many days will all of them together complete the remaining work?

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Explanation:

Work complete by 12 men in 14 days = 12*14/(24*16) = 7/16
So, Remaining work = 9/16
Work complete by 12 men & 12 children = (12/(24*16)) + 12/(48*16) = (1/32 + 1/64) = 3/64
No. of days = (work complete by 12 men & 12 children / remaining work).
= (3/64)/(9/16) =

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69. A printer started its work at 8.15 a.m. and ended its work at 9.20 p.m. It was interrupted twice for the time duration of 42 min. It can print 100 instructions per hour. Approximate how many instructions it can print?

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Explanation:

Time duration from 8.15 am to 9.20 pm = 13 hours 5 min = 785 minutes
stoppage for 2*42 min= 84 min
effective running time = 701 min
in 60 min 100 instructions are printed
in 1 min = 100/60 instructions
in 701 min , we have 701*100/ 60 = 1168.33 instructions

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70. A printer can print 17000 billing statements in an hour .one day, the printer began printing at 1.26 A.M, the printing was interrupted twice.for 50 mins each time .the job was finished at 6.06 pm. How many statements did the printer?

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Explanation:

1:26-6.06= 16.80 hrs. = 1040 minutes
Printer was interrupted twice for 2 minutes
there for 50*2=100 minutes
printed worked for 1040-100 = 940 minutes.
60 minutes----------17000 statements
1 minute--------------17000/60
940 minutes-------- 17000 x 940/60 = 266,333 statements per minute

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