A can do a job in 24 days, B in 9 days and C in 12 days. B and C together start the work but leave after 3 days. How much time was taken A to complete remaining work ?

A 7 days

B 9 days

C 10 days

D 12 days

Correct Answer: Option C

Solution:

B+C can do in 1 day = \(\frac{1}{9} + \frac{1}{{12}} = \frac{{4 + 3}}{{36}} = \frac{7}{{36}}\)

B+C can do in 3 days = \(\frac{{7 \times 3}}{{36}} = \frac{7}{{12}}\)

Remaining part = \(1 - \frac{7}{{12}} = \frac{5}{{12}}\)

1 part is done by A = 24 day

5/12 part is done by A = \(24 \times \frac{5}{{12}}\) = 10 days