# Multiple Groups : Time and Work Questions

Question 01

Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of man and a woman?

20 women can complete the work in 16 days.
So, 1 woman can complete the work in (20 × 16) = 320 days.
Thus, 1 woman’s 1 day work = 1/320

16 men can complete the work in 15 days.
1 man can complete the work in (15 × 16) = 240 days.
Thus, 1 man’s 1 day work = 1/240

Ratio of capacity of man and woman = 1/320 : 1/240 = 4:3

Question 02

10 men can complete a piece of work in 15 days and 15 women can complete the same work in 12 days. If all the 10 men and 15 women work together, in how many days will the work get completed?

Let any work is 60 units.

10 men 15 days work= 60 units
10 men 1 day work= 60/15
Thus, 10 men = 4 unit / day

Similarly,
15 women = 5 unit / day.

If all of them work together, work done (10 men + 15 women) = (5 + 4) = 9 unit / day.

Thus, work to be completed =  60 unit / 9 unit per day = 20/3 days = 6 days
Hence, in 6 days work will get completed

Question 03

Three men, four women and six children can complete a work in seven days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days?

Let 1 woman’s 1 day work = x
Then, 1 man’s 1 day work = x/2 and 1 child’s 1 day work = x/4

So, 3x/2+ 4x + 6x/4 = 1/7

28x/4 = 1/7

X = 1/49

Thus, 1 woman alone can complete the work in 49 days.
So, to complete the work in 7 days, number of women required = 49/7 = 7

Question 04

12 men can complete a piece of work in 4 days, while 15 women can complete the same work in 4 days. 6 men start working on the job and after working for 2 days, all of them stopped working. How many women should be put on the job to complete the remaining work, if it is to be completed in 3 days?

Let the productivity of man be m and the productivity of woman be w.
Thus,
12m × 4 = 15w × 4
4m = 5w
m = 5/4 w

Total work done by women = 60w

Work done by 6 men in 2 days = 6m × 2 = 6 × 5/4 × 2 = 15w
Thus, remaining work = 60w – 15w = 45w

Let F women complete the remaining job in 3 days.
Thus, Fw × 3 = 45w
F = 45/3 = 15

Thus, 15 women are required to complete the job.

Question 5

If 12 men and 16 boys can do a piece of work in 5 days; 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is:

Let 1 man’s 1 day’s work = x and
1 boy’s 1 day’s work = y

As 12 men and 16 boys complete whole work in 5 days
so, their one day work can be represented as
12 x + 16 y = 1/5………………….. (i)

Similarly,
13x + 24 y = ¼…………………… (ii)

Multiplying eq (i) by 3 and eq (ii) by 2, we get-

36 x + 48 y = 3/5 ……………… (iii)

26 x + 48 y = ½………………… (iv)

Subtracting eq (iv) from eq (iii); we get-

10 x = 3/5 – ½

x = 1/100

Putting x = 1/100 in eq (i), we get – y = 1/200

Therefore, required ratio = x : y = 1/100 : 1/200 = 2:1