A can finish a work in $12$ days and B in $18$ days. If they work together for $4$ days, what fraction of the work remains?

Question

A can finish a work in $12$ days and B in $18$ days. If they work together for $4$ days, what fraction of the work remains?

Option A

$\frac13$

Option B — Correct answer

$\frac49$

Correct choice.

Option C

$\frac59$

Option D

$\frac23$

Explanation

Joint rate $=\frac1{12}+\frac1{18}=\frac5{36}$. Work done in $4$ days $=\frac{20}{36}=\frac59$. Remaining work $=1-\frac59=\frac49$.

Chapter Mock 7: Time and Work, Pipe and Cistern