Question

A can do a piece of work in 20 days while B can do it in 15 days. With the help of C, they finish the work in 5 days. In what time would C alone do it?​

Answer 1

$\bf\large\underline{\underline{ Given :- }}$

• A can do a piece of work in 20 days

• B can do it in 15 days

• with help of C they did the work in 5 days

$\bf\large\underline{\underline{ To \: Find:- }}$

• Find the time required by C for doing the work alone

$\bf\large\underline{\underline{ Answer :- }}$

• A $\red{ \implies}$ 20 days

• B $\red{ \implies}$ 15 days

• A + B + C = 5 days

• $\\ \bf \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{1}{5}$

• $\bf\frac{1}{20} + \frac{1}{15} + \frac{1}{c} = \frac{1}{5}$

• $\\ \bf\frac{1}{c} = \frac{1}{5} - (\frac{1}{20} + \frac{1}{15} )$

• $\\ \bf\frac{1}{c} = \frac{1}{5} - \frac{7}{60}$

• $\\ \bf \frac{1}{c} = \frac{1}{12}$

• $\\ \bf c = 12$

$\rule{10cm}{0.05cm}$

C takes 12 days to complete the work alone.