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A, B and C together can do a piece of work in 14 days, whereas C alone can do the same work in 42 days. How long will A and B together take to finish
Question

A, B and C together can do a piece of work in 14 days, whereas C alone can do the same work in 42 days. How long will A and B together take to finish it?

A.

28 days

B.

35 days

C.

21 days

D.

7 days

Correct option is C

Given:

A, B, and C together can complete the work in 14 days

C alone can complete the work in 42 days

Formula Used:

Work per day = 1Number of days \frac{1}{\text{Number of days}} ​​

Solution:

A + B + C's 1 day work = 114\frac{1}{14}​​

C's 1 day work = 142\frac{1}{42}​​

Then,

A + B = 114142 \frac{1}{14} - \frac{1}{42}​​

=3142= \frac{3 - 1}{42}​​

=242= \frac{2}{42}​​

=121= \frac{1}{21}​​

So, A and B together can complete the work in 21 days.

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