Question

5 men and 12 boys finish a piece of work in 4 days , 7 men and 6 boys do it in 5 days ratio between the efficiency of a man and boy is

Pls give me full explanation with each steps

Answer 1

Let the amount of work done by 1 man in 1 day = m

Let the amount of work done by 1 boy in 1 day = b

Let the work to be done = x

Work done per day by 5 men is 5m and 12 boys is 12b.

Total work done by men and boys per day = 5m+12b

For 4 days = 4*(5m+12b)

This is equal to x.

So x = 4*(5m+12b)

Similarly in second case :

x = 5*(7m+6b)

Equating the RHS since LHS is same for both equations,

4*(5m+12b) = 5*(7m+6b)

20m + 48b = 35m + 30b

Therefore 15m = 18b

m/b = 18/15

= 6/5

Therefore the ratio is 6:5