A can do a piece of work in 16 days and B in 24 days. They take the help of C and three together finish the work in 6 days. If the total remuneration for the work is 400. The amount (in rupees) each will receive, in proportion, to do the work is

It is given that A , B can do a work in 16, 24 days respectively

and together with C, A and B can do the same work in 6 days

Let assume that amount of work = 48 units (LCM of 6,16,24)

A's 1 day work = $$\frac{48}{16}$$ = 3 units

B's 1 day work = $$\frac{48}{24}$$ = 2 units

(A + B + C)'s 1 day work = $$\frac{48}{6}$$ = 8 units

C's 1 day work = 8 - (3+2) = 3 units.

So number of days required by C to complete 48 units of work = $$\frac{48}{6}$$ = 8 days

Now in 6 days ratio of units of work done in 6 days by A:B:C = (6 x 3):(6 x 2):(6 x 3) = 3 : 2 : 3

So out of total remuneration of Rs 400

A's share = $$\frac{3}{8}$$ x 400 = Rs 150

B's share = $$\frac{2}{8}$$ x 400 = Rs 100

C's share = $$\frac{3}{8}$$ x 400 = Rs 150