Question

Three men can do as much work as 5 boys and the wages of 3 boys are equal to those of 2 men. A work on which 40 boys and 15 men are employed takes 8 weeks and costs Rs 15750. How long would it take if 20 boys and 20 men were employed , and how much would it costs?

Answer 1

men work = 5 boys work

so let work done by 1 boy in 1 day = 1/5;

then work done by 1 man in 1 day = 1/3;

so total work done in 8 weeks = work done by boys + work done by men

= 1/5*40*8*7 +1/3*15*8*7

=13*56;...........................................................................(i)

now let wage of 1 boy for 1 day = x;

wage of 1 man for 1 day =y;

so a/c quest,

3*x=2*y................................................(ii)

now

(8*7)(40*x+15*y)=15750.........................................(iii)

from (ii) and (iii)

x=(15750*2)/(56*125);

x=4.5;

y=6.75;

now... no. of dys taken by 20b and 20m to finish the work=z

z*(1/5*20+1/3*20) = 13*56;

z=(13*56*15)/20*8;

z=39*7/4;

z=9.75 week;

total amount....

20(4.5*9.75*7 + 6.75*9.75*7) .............(wage of boy=4.5; wage of men =6.75)

= 20(307.125 + 460.687)

= 15356.25.

so ans total time = 9.75 week and amount =15356.25.