# Time and Work Problems – Multiple Groups 02

In this post we will try to solve time and work questions with step by step solutions.
The main focus of this module is to solve questions which involve multiple group of people like men, women and children.

These types of time and work problems are repeatedly asked in quantitative aptitude section of competitive examinations like SSC-CGL, SSC-CHSL, NDA, AFCAT, SBI-PO, IBPS, GMAT, CAT etc.
So its better to be prepared and accustomed to the types of question asked in the module.

(01) If 1 man or 2 women or 3 boys can complete a piece of work in 88 days, then 1 man, 1 woman and 1 boy together will complete it in:

Sol: 1 man = 2 women = 3 boys

1 man + 1 woman + 1 boy = ( 3 + 3/2 + 1 ) boys = 11/2 boys

Required no. of days = ( 3 × 2 × 88 ) / 11= 48 days

(02) 2 men and 3 women together or 4 men can complete a piece of work in 20 days. 3 men and 3 women will complete the same work in:

Given:
2 Men and 3 Women complete the work in 20 days
Also, 4 Men complete the same work in 20 days

Hence,
==> 2m + 3w = 4m
==> 3w = 4m – 2m = 2m
==> 3w = 2m

==> 3w + 3m = 2m + 3m
==> 3m + 3w = 5m — eq (1)
Through above equation we understood that work of 3 men and 3 women together is equivalent to work of 5 men.

We know that
4 men can do work in 20 days.
1 man can do work in ( 4 × 20 ) days
5 men can do work in ( 4 × 20 ) / 5 = 16 days

hence from eq (1) now we know that it will take 16 days for 3 man and women to complete the work

(03) 20 men or 24 women can complete a piece of work in 20 days. If 30 men and 12 women undertake to complete the work, the work will be completed in:

Sol:
Both 20 men or 24 women complete the same work in 20 days
==>20 men = 24 women
==> 5 men = 6 women
Multiplying by 2 we get
==> 10 men = 12 women — eq(1)

we have to find time taken by 30 men and 12 women
30 men + 12 women = 30 men + 10 men (using equation 01)
30 men + 12 women = 40 men —– eq(2)

Thus, M1 D1 = M2 D2

20 × 20 = 40 × D2

D2 = 20 × 20 / 40 = 10 days

Time taken by 40 men = 10 days
By equation (2), we can say that 30 men and 12 women will take 10 days to complete the work

(04) 6 men and 8 women can do a piece of work in 10 days. Then, 3 men and 4 women can do the same work in?

6 Men and 8 women together complete the work in 10 days
==> 6m + 8w = 1/10

Multiplying 1/2 on both sides
==> ½ ( 6m + 8w ) = ½ × 1/10 = 1/20

==> 3m + 4w = 1/20

Thus, 3 men and 4 women can do the same work in 20 days.

(05) If 10 men or 20 women or 40 children can do a piece of work in 7 months, then 5 men, 5 women and 5 children together can do half of the work in how many days?

Let total work be W.

Work done by 1 man in 1 month = W / 10 × 7 = W / 70
Work done by 1 woman in 1 month = W / 20 × 7 = W / 140
Work done by 1 child in 1 month = W / 40 × 7 = W / 280

Total work done by 5 men, 5 women and 5 children in 1 month = 5W / 70 + 5W / 140 + 5W / 280 = W / 8

Let number of months be n to complete half of the work.

5 Men, 5 Women and 5 Children will complete half of the work in:

Work done by 5 Men, 5 Women and 5 Children in 1 month * number of month = Half of work
==> W / 8 × n =  W / 2
==> n = 4

Hence 4 month will be the total time taken

(06) 15 men can finish a piece of work in 20 days, however it takes 24 women to finish it in 20 days. If 10 men and 8 women undertake to complete the work, then they will take?

15 men finish the work in 20 days
Hence, 15 men’s 1 day work = 1/20

24 women finish the work in 20 days
Hence, 24 women’s 1 day work = 1/20

From the above statement we can say that;
1 man’s 1 day work = 1/(15*20) => 1/300
and 1 woman 1 day’s work = 1/(24*20) => 1/480

10 men and 8 women’s 1 day work = 10 / 300 + 8 / 480 = 1 / 30 + 1 / 60 = 2 + 1 / 60 = 3 / 60 = 1 / 20

So 10 men and 8 women can complete the work in 20 days