A and B can complete a piece of work in 20 days, B and C can complete the same piece of work in 12 days, while C and A can do it in 15 days. In how many days can A, B, and C together complete the same work?

Correct option is C

Given:

A and B can complete a work in 20days

B and C can complete the work in 12days

A and C can complete the work in 15 days

Formula Used:

Let total work be 1.

Then work done 1 day $$=\frac{1}{Total\ time\ to\ work}$$​​

Solution:

A and B’s one day work =$$\frac{1}{A} +\frac{1}{B} = \frac{1}{20}$$​    ….(1)

B and C’s one day work $$=\frac{1}{B} + \frac{1}{C} = \frac{1}{12}$$​     …(2)

A and C’s one day work= $$\frac{1}{A} + \frac{1}{C} =\frac{1}{15}$$​     ….(3)

Adding all the equations we get

​$$2 \left(\frac{1}{A} + \frac{1}{B} + \frac{1}{C} \right)’s \text{ one day work}: \\ \ \\ = \frac{1}{20} + \frac{1}{12} + \frac{1}{15} =\frac{3+5+4}{60} =\frac{12}{60} =\frac{1}{5}$$​​

(A+B+C)’s one day work = $$\frac{1}{10}$$​​

A,B and C can complete the work in = $$\frac{1}{\frac{1}{10}}$$ = 10 days