# 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:

50 men can build a tank in 40days, but though they begin the work together, 5 men quit every ten days. The time needed to build the tank is ?

 A) 50 days B) 48 days C) 47.5 days D) 49 days

Explanation:

50 men can build a tank in 40 days

Assume 1 man does 1 unit of work in 1 day

Then the total work is 50×40 = 2000 units

50 men work in the first 10 days and completes 50×10 = 500 units of work

45 men work in the next 10 days and completes 45×10 = 450 units of work

40 men work in the next 10 days and completes 40×10 = 400 units of work

35 men work in the next 10 days and completes 35×10 = 350 units of work

So far 500 + 450 + 400 + 350 = 1700 units of work is completed and

Remaining work is 2000 - 1700 = 300 units

30 men work in the next 10 days. In each day, they does 30 units of work.

Therefore, additional days required = 300/30 =10

Thus, total 10+10+10+10+10 = 50 days required.

10 1303
Q:

6 men can complete a piece of work in 12 days. 8 women can complete the same piece of work in 18 days whereas 18 children can complete the piece of work in 10 days. 4 men, 12 women and 20 children work together for 2 days. If only men were to complete the remaining work in 1 day how many men would be required totally?

 A) 38 B) 72 C) 36 D) 76

Explanation:

Given 4men, 12 women and 20 children work for  2 days.

Workdone for 2 days by 4men, 12 women and 20 children =

Therefore, remaining work = 1 - $\frac{1}{2}$ = $\frac{1}{2}$

To complete the same work by only men in 1 day,

We know that M1 x D1 = M2 x D2

Here M1 = 6 , D1 = 12 and M2 = M , D2 = 1

12 x 6 = M x 1

=> M = 12 x 6 = 72

=> But the remaining work = 1/2

Men required => 1/2 x 72 = 36

Only men required to Complete the remaining work in 1 day = 36.

8 1274
Q:

Sixty men can stitch 150 shirts in 30 days working 8 hours a day. In how many days can 35 men stitch 200 shirts working 6 hours a day ?

 A) 87.5 B) 89 C) 91.5 D) 93.5

Explanation:

We have M1 D1 H1 / W1 = M2 D2 H2 / W2 (Variation rule)
(60 x 30 x 8)/ 150 = (35 x D2 x 6) / 200
D2 = (60 x 30 x 8 x 200) / (150 x 35 x 6) => D2 = 91.42 days =~ 91.5 days.

4 1224
Q:

Two boys and a girl can do a work in 5 days, while a boy and 2 girls can do it in 6 days. If the boy is paid at the rate of 28$a week, what should be the wages of the girl a week ?  A) 24$ B) 22 $C) 16$ D) 14 $Answer & Explanation Answer: C) 16$

Explanation:

Let the 1 day work of a boy=b and a girl=g, then
2b + g = 1/5 ---(i) and
b + 2g = 1/6 ---(ii)
On solving (i) & (ii), b=7/90, g=2/45
As payment of work will be in proportion to capacity of work and a boy is paid $28/week, so a girl will be paid $28×\frac{\frac{2}{45}}{\frac{7}{90}}$ = 16$.

5 1210
Q:

In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?

 A) 145 B) 165 C) 175 D) 135

Explanation:

Given that,

working days = 5

working hours = 8

A man get rupess per hour is Rs.2.40

So in one day the man get total rupees is 2.40 x 8 = 19.2

So in 5 days week the man get total rupees is 19.2 x 5 = 96

So in 4 week the man get total rupees is 96 x 4 = 384

So the man worked for = 160hours in 4 weeks

But given that the man earned Rs.432

Hence remaning money is (432-384 = 48)which is earn by doing overtime work

Overtime hours  = 48/3.20 = 15

So total worked hours is = 15 + 160 = 175.

3 1195
Q:

A is 3 times faster than B. If A can finish a work 32 days less than that of B, find the number of days need to finish the work if both are working together?

 A) 12 days B) 24 days C) 32 days D) 16 days

Explanation:

It is given that efficiency ratio =3:1

so time ratio will be 1:3 (since work is same)

Also given that time diff = 32 days. ratio difference = 3-1 =2

2 ratio = 32 days

1 ratio = 16 days.

So A will alone finish it in 16 days and B will finish it in 16*3 = 48 days.

Total work = LCM of 16 and 48 = 48.

Total time = Total work/Total efficiency

ie; 48/4= 12 days.

2 1194
Q:

A certain job was assigned to a group of women to do it in 20 days. But 12 women did not turn up for the job and the remaining did the job in 32 days. The original number of women in the group was?

 A) 36 B) 32 C) 22 D) 28

Explanation:

Let the total women in the group be 'W'

Then according to the given data,

W x 20 = (W-12) x 32

=> W = 32

Therefore, the total number of women in the group = 32

6 1174
Q:

P is 30% more efficient than Q. How much time will they, working together, take to complete a job which P alone could have done in 23 days?

 A) 16 days B) 13 days C) 15 days D) 12 days

Explanation:

Ratio of times taken by P & Q = 100 : 130 = 10:13

Let Q takes x days to do the work

Then, 10:13 :: 23:x

=> x = 23x13/10

=> x = 299/10

P's 1 day's work = 1/23

Q's 1 day's work = 10/299

(P+Q)'s 1 day's work = (1/23 + 10/299) = 23/299 = 1/13

Hence, P & Q together can complete the work in 13 days.