Question

if 6men and 8boys can do a piece of work in a 10 days while 26 men and 48 boys can do the same work in 2 days the time taken by 15 men and 20 boysin doing the same type of work will be

Answer 1

Let M denotes the work done by a man in 1 day and B denotes the work done by a boy in 1 day.

Now, 6 men and 8 boys do the work in 10 days means 10(6M+8B) = 1

Similarly, 26 men and 48 boys do the work in 2 days means 2(26M+48B) = 1

=> 10(6M+8B) = 2(26M+48B)

=> 60M + 80B = 52M + 96B

=> 8M = 16B

=> 1M = 2B

Thus, if we employ 15 men and 20 boys, we mean to say; 15M + 20B

= 30B + 20B = 50B.

Now, (6M + 8B) do the work in 10 days.

=> (12B + 8B) do the work in 10 days.

=> 20B do the work in 10 days.

=> 1B do the work in 10×20 = 200 days.

=> 50B will do the work in 200/50 = 4 days.

Answer 2

let time taken by men=x
time taken by boy=y
1/6x+1/8y=1/10
1/26x+1/48x=1/5
put the values of x and y in
1/15x+1/20y=will be the ans