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?Options4 days5 days6 days7 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 first piece of information, we know that 6 men and 8 boys can do the work in 10 days. This can be written as:

6M + 8B = 1/10 (since the work done is 1 and they complete it in 10 days)

From the second piece of information, we know that 26 men and 48 boys can do the work in 2 days. This can be written as:

26M + 48B = 1/2

We now have a system of two equations that we can solve for M and B.

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

Subtracting this from the second equation gives us -4M + 8B = 0, or B = 0.5M.

Substituting B = 0.5M into the first equation gives us 6M + 4M = 1/10, or 10M = 1/10, or M = 1/100.

Substituting M = 1/100 into B = 0.5M gives us B = 0.5/100 = 1/200.

So, the work rate of a man is 1/100 per day and the work rate of a boy is 1/200 per day.

Finally, we can find out how long it would take 15 men and 20 boys to do the work.

The combined work rate of 15 men and 20 boys is 15/100 + 20/200 = 0.15 + 0.10 = 0.25 per day.

Therefore, it would take them 1/0.25 = 4 days to complete the work.

So, the correct answer is 4 days.