Question

A and B can do a piece of work in $40$ days, B and C in $30$ days, and C and A in $24$ days. How long does it take if they work on it together?

• A. $14$ days
• B. $30$ days
• C. $20$ days
• D. $18$ days

Answer 1

The correct option is C $20$ days

Given A and B do work in 40 days.and Band C do work in 30 days and C and A do work in 24 days

Then, A and B one day work =$\frac{1}{40}$

B and C one day work =$\frac{1}{30}$

C and A one day work =$\frac{1}{24}$

Summing up the above three equations give,

2( A+B+C) one day work =$\frac{1}{40}+\frac{1}{30}+\frac{1}{24}=\frac{60}{600}=\frac{1}{10}$

So A+B+C one day work =$\frac{1}{20}$

$\therefore$ A, B and C can do the work together in 20 days