# Time and Work Questions

FACTS  AND  FORMULAE  FOR  TIME  AND  WORK  QUESTIONS

1. If A can do a piece of work in n days, then A's 1 day's work =$\frac{1}{n}$

2. If A’s 1 day's work =$\frac{1}{n}$, then A can finish the work in n days.

3. A is thrice as good a workman as B, then:

Ratio of work done by A and B = 3 : 1.

Ratio of times taken by A and B to finish a work = 1 : 3.

NOTE :

Hence,

Whole work is always considered as 1, in terms of fraction and 100% , in terms of percentage.

In general, number of day's or hours = $\frac{100}{Efficiency}$

Q:

4 men can repair a road in 7 hours. How many men are required to repair the road in 2 hours ?

 A) 17 men B) 14 men C) 13 men D) 16 men

Explanation:

M x T / W = Constant
where, M= Men (no. of men)
T= Time taken
So, here we apply
M1 x T1/ W1 = M2 x T2 / W2
Given that, M1 = 4 men, T1 = 7 hours ; T2 = 2 hours, we have to find M2 =?
Note that here, W1 = W2 = 1 road, ie. equal work load.
Clearly, substituting in the above equation we get, M2 = 14 men.

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40 35786
Q:

A works twice as fast as B.If  B can complete a work in 18 days independently,the number of days  in which A and B can together finish the work is:

 A) 4 days B) 6 days C) 8 days D) 10 days

Explanation:

Ratio of rates of working of A and B =2:1. So, ratio of times taken =1:2

Therefore, A's 1 day's work=1/9

B's 1 day's work=1/18

(A+B)'s 1 day's work= 1/9 + 1/18 = 1/6

so, A and B together can finish the work in 6 days

Filed Under: Time and Work

100 32603
Q:

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?

 A) 18 days B) 24 days C) 30 days D) 36 days

Explanation:

2(A+B+C)'s 1 day work = 1/30 + 1/24 + 1/20 = 1/8

=>(A+B+C)'s  1 day's work= 1/16

work done by A,B and C in 10 days=10/16 = 5/8

Remaining work= 3/8

A's 1 day's work= $116-124=148$

Now, 1/48 work is done by A in 1 day.

So, 3/8 work  wil be done by A in =48 x (3/8) = 18 days

Filed Under: Time and Work

138 32516
Q:

10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?

 A) 215 days B) 225 days C) 235 days D) 240 days

Explanation:

Given that

(10M + 15W) x 6 days = 1M x 100 days

=> 60M + 90W = 100M

=> 40M = 90W

=> 4M = 9W.

From the given data,

1M can do the work in 100 days

=> 4M can do the same work in 100/4= 25 days.

=> 9W can do the same work in 25 days.

=> 1W can do the same work in 25 x 9 = 225 days.

Hence, 1 woman can do the same work in 225 days.

43 32117
Q:

(x-2) men can do a piece of work in x days and (x+7) men can do 75% of the same work in (x-10)days. Then in how many days can (x+10) men finish the work?

 A) 27 days B) 12 days C) 25 days D) 18 days

Explanation:

$34×(x-2)x=(x+7)(x-10)$

=> x= 20   and   x=-14

so, the acceptable values is x=20

Therefore, Total work =(x-2)x = 18 x 20 =360 unit

Now   360 = 30 x k

=> k=12 days

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77 31144
Q:

The ratio of efficiency of A is to C is 5:3. The ratio of number of days taken by B is to C is 2:3. A takes 6 days less than C, when A and C completes the work individually. B and C started the work and left after 2 days. The number of days taken by A to finish the remaining work is:

 A) 4.5 B) 5 C) 6 D) 9 1/3

Explanation:

A   :   C

Efficiency      5    :   3

No of days   3x   :  5x

Given that, 5x-6 =3x  => x = 3

Number of days taken by A = 9

Number of days taken by C = 15

B  :  C

Days   2  :  3

Therefore, Number of days taken by B = 10

Work done by B and C in initial 2 days = $2110+115$= 1/3

Thus,  Rest work =2/3

Number of days required by A to finish 2/3 work = (2/3) x 9 = 6 days

Filed Under: Time and Work

81 29766
Q:

A Contractor employed a certain number of workers  to finish constructing a road in a certain scheduled time. Sometime later, when a part of work had been completed, he realised that the work would get delayed by three-fourth of the  scheduled time, so he at once doubled the no of workers and thus he managed to finish the road on the scheduled time. How much work he had been completed, before increasing the number of workers?

 A) 10 % B) 14 ( 2/7 )% C) 20 % D) Can't be determined

Explanation:

Let he initially employed x workers which works for D days and he estimated 100 days for the whole work and then he doubled the worker for (100-D) days.

D * x +(100- D) * 2x= 175x

=>  D= 25 days

Now , the work done in 25 days = 25x

Total work = 175x

Therefore, workdone before increasing the no of workers = $25x175x×100$ % = $1427%$

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106 28904
Q:

A and B can do a piece of work in 40 and 50 days. If they work at it an alternate days with A beginning in how many days, the work will be finished ?

(A+B)'s two days work = $140+150=9200$

Evidently, the work done by A and B duing 22 pairs of days

i.e in 44 days = $22×9200=198200$

Remaining work = $1-198200$= 1/100

Now on 45th day A will have the turn to do 1/100 of the work and this work A will do in $40×1100=25$

Therefore,  Total time taken = 44$25$daya