Question

a can finish a work in 12 days and b can do it in 15 days after a had work for 3 days, b also join a to finish the remaining work in how many days the remaining work will be finished ?

Answer 1

A can do the piece of work in 12 days.
One day work of A =1/12
B can do the piece of work in 15 days
One day work of B=1/15
Together 1 day work =
$= \frac{1}{12} + \frac{1}{15} \\ = \frac{5 + 4}{60} \\ = \frac{9}{60}$
$= \frac{3}{20}$
A worked for 3 days=
$\frac{1}{12} \times 3 = \frac{1}{4}$
Remain work =
$= 1 - \frac{1}{4} \\ = \frac{4 - 1}{4} \\ = \frac{3}{4}$
So,the remain work will be done in=
$\frac{3}{4} \div \frac{3}{20} \\ \frac{3}{4} \times \frac{20}{3} \\ = 5$
Hence,
the remain work will be done in = 5 days.