Question

A can do a work in 15 days and B in 20 days. If they work on it together for 4 days then the fraction of the work that is left is:

• A. $\frac{1}{4}$
• B. $\frac{1}{10}$
• C. $\frac{7}{15}$
• D. $\frac{8}{15}$

Answer 1

The correct option is D

$\frac{8}{15}$

A’s 1 day’s work = $\frac{1}{15}$;
B’s 1 day’s work = $\frac{1}{20}$.

(A+B)’s 1 day’s work = $(\frac{1}{15}+\frac{1}{20})=\frac{7}{60}$

(A+B)’s 4 days’ work = $(\frac{7}{60}\times 4)=\frac{7}{15}$

Remaining work will be the difference between the whole work and the work done by both in 4 days.

∴ Remaining work = $(1-\frac{7}{15})=\frac{8}{15}$