Select the correct answerIf 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, then the time taken by 15 men and 20 boys to do the same type of work will be?Options5 days6 days7 days4 days

The problem can be solved by setting up equations based on the information given and then solving for the unknowns.

Let's denote the work rate of a man as M and the work rate of a boy as B.

From the problem, we know that:

1. 6M + 8B = 1/10 (since 6 men and 8 boys can complete the work in 10 days)

2. 26M + 48B = 1/2 (since 26 men and 48 boys can complete the work in 2 days)

We can solve this system of equations to find the values of M and B.

Multiplying the first equation by 5 gives us 30M + 40B = 1/2.

Subtracting the second equation from this result gives us 4M - 8B = 0, or M = 2B.

Substituting M = 2B into the first equation gives us 6(2B) + 8B = 1/10, or 20B = 1/10, so B = 1/200 and M = 1/100.

Finally, we can find out how long it would take 15 men and 20 boys to do the work by using the equation 15M + 20B = 1/T, where T is the time in days.

Substituting the values of M and B gives us 15(1/100) + 20(1/200) = 1/T, or 0.15 + 0.10 = 1/T, so 1/T = 0.25 and T = 4 days.

So, the correct answer is 4 days.