Question

A, B and C can do a work in 6, 8 and 12 days respectively. If they do the work together and earn Rs. 2700, what is the share of C in that amount ?

• A. 600
• B. 900
• C. 1000
• D. 700

Answer 1

The Correct Option is A

To determine the share of C, let's first calculate the individual work rates of A, B, and C in terms of work done per day:

• A's rate: \( \frac{1}{6} \) work per day
• B's rate: \( \frac{1}{8} \) work per day
• C's rate: \( \frac{1}{12} \) work per day

When they work together, their combined work rate is:

\[\frac{1}{6}+\frac{1}{8}+\frac{1}{12}=\frac{4}{24}+\frac{3}{24}+\frac{2}{24}=\frac{9}{24}=\frac{3}{8}\]

Thus, they complete \( \frac{3}{8} \) of the work in one day. The total work is completed in:

\[\frac{1}{\frac{3}{8}}=\frac{8}{3}\text{ days}\]

The amount earned for the complete work is Rs. 2700, to be divided based on their individual contribution to the work:

Contribution of C:

\[\text{C's work rate} \times \text{total time} = \frac{1}{12} \times \frac{8}{3} = \frac{2}{9}\]

C's share of the total amount:

\[\frac{2}{9} \times 2700 = 600\]

Therefore, C's share is Rs. 600.