# If 6 men and 8 boys can do a piece of work in 10 days and 26 men and 48 boys :

If 6 men and 8 boys can do a piece of work in 10 days and 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys to do the same type of work will be-

- 5 days
- 4 days
- 6 days
- 7 days

**Answer: (2) 4 days **

**Explanation:-**

Let a man takes X days to complete the work and a boy takes Y days to complete the work.

So, Work do be by a man in 1 day = 1/X

and, work done by a boy in 1 day = 1/Y

Given 6 men and 8 boys can do the work in 10 days

So, Work done by 6 men and 8 boys in 1 day = 1/10

=> 6/X + 8/Y = 1/10 ———————– (1)

Also, given that 26 men and 48 boys can do the work in 2 days

So, Work done by 26 men and 48 boys in 1 day = 1/2

26/x + 48/y = 1/2 ———————– (2)

6 x (1) – (2) gives:

10/X = 1/10

X = 100

Putting the value of x in (1) we get Y = 200

So 1 man can complete the work in 100 days and 1 bot can complete the work in 200 days.

So, work do be by 1 man in a day = 1/100

=> Work do be by 15 men in a day = 15/100 = 3/20

Work do be by 1 boy in a day = 1/200

Work do be by 20 boy in a day = 20/200 = 1/10

work done by 15 men and 20 boys in 1 day = 3/20 + 1/10 = 1/4

So, 15 men and 20 boys can complete the work in 4 days

Hence, the correct answer is option (2) 4 days.