Question

The number of days in which a and b together can finish a piece of work is 12 days less than the time taken by a alone and 27 days less than the time taken by b alone to finish the work. if a and b completed the work in 15 days with the help of c and got a total compensation of rs 3000 for the work, then what is the share of c?

Answer 1

let the no. of days in which work has been completed by A and B be X then A takes (X + 12) days and B takes (X +27 ) day to finish the work .
ATQ :-
1/X+12 + 1/ X +27 = 1/X
X[( X + 12) + (X + 27)]= (X+ 12)(X+ 27)
(X)square =324
X= 18
So, if the total work is 1 unit then the work done by both A and B together in one day will be 1/18 unit . So total work done by these 2 in 15 days =15/18=5/6th work
So, the work done by C is 1/6th of the total work
So, the work which C will get = 1/6th of the total work .
So, the money which C will get = 1/6×3000=500