Question

Three persons A, B and C work together
on a job and finish it in 18 days. If A and B
working together can finish the job in 45
days, find how long C working alone would
take to complete it.​

Answer 1

Solution:-

Given:-

A, B and C together complete the work in 18 days.

A and B complete the work in 45 days.

To Find:-

Time required for C to complete the work alone.

By the Problem:-

A, B and C together complete the work in 18 days.

So, In 1 day they can complete $\frac{1}{18} th \: of \: work.$

A and B complete the work in 45 days.

So, In 1 day A and B can complete $\frac{1}{45} th \: of \: work$

According to the question:-

$= > (A + B + C) = \frac{1}{18} part \\ = > (A + B) = \frac{1}{45}part \\ = >In \: 1 \: day \: C \: can \:do= (A + B + C) - (A + B)part \\ = > \frac{1}{18} - \frac{1}{45} part\\ => \frac{5 - 2}{90} part \\ = > \frac{3}{90} \: part$

So, C takes= $\frac{90}{3} = 30 \: days$