Question

$25$ men with $10$ boys can do in $6$ days as much work as $21$ men with $30$ boys can do in $5$ days. How many boys must help $40$ men to do the same work in $4$ days?

Answer 1

Let the amount of work done by a Man and a Boy in a day be m and b, respectively.

Then, as per the question

6(25m + 10b) = 5(21m + 30b)

Or, 150m + 60b = 105m + 150b

Or, 45m = 90b

Or, m = 2b……… (i)

Now, the total amount of work

= 150 m + 60b

= 360b (substituing m from i)……(ii)

Now, let the number of boys needed be x.

So,

4(40m + xb) = 360b

Or, 80b + xb = 90b

Or, x = 10.

So, 10 boys will be needed.