A can do a piece of work in 16 days and B in | vedclass

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(A) Work done by $A$ in $1$ day $= 1/16$.Work done by $B$ in $1$ day $= 1/24$.Work done by $A, B,$ and $C$ in $1$ day $= 1/6$.Work done by $C$ in $1$

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$A: 150, B: 100, C: 150$

Vedclass · Answer

(A) Work done by $A$ in $1$ day $= 1/16$.Work done by $B$ in $1$ day $= 1/24$.Work done by $A, B,$ and $C$ in $1$ day $= 1/6$.Work done by $C$ in $1$ day $= (A+B+C)$'s $1$ day work $- (A+B)$'s $1$ day work.$1/C = 1/6 - (1/16 + 1/24) = 1/6 - (3+2)/48 = 1/6 - 5/48 = (8-5)/48 = 3/48 = 1/16$.The ratio of work done by $A, B,$ and $C$ is $1/16 : 1/24 : 1/16$.To simplify,multiply by $48$: $48/16 : 48/24 : 48/16 = 3 : 2 : 3$.Total parts $= 3 + 2 + 3 = 8$.Share of $A = (3/8) 	imes 400 = Rs. 150$.Share of $B = (2/8) 	imes 400 = Rs. 100$.Share of $C = (3/8) 	imes 400 = Rs. 150$.

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

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