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

Hint:

The share ratio equals the daily-work-rate ratio: 4:3:2.

Answer 1

The Correct Option is A

Step 1: Write each person's one day work as a fraction.
$A$ does $1/6$ of the work per day, $B$ does $1/8$ per day, and $C$ does $1/12$ per day.

Step 2: Add these fractions to get the combined one day work.
$1/6 + 1/8 + 1/12$. Using 24 as the common denominator: $4/24 + 3/24 + 2/24 = 9/24 = 3/8$.

Step 3: Find what fraction of the combined work belongs to C.
$C$'s share of the daily work is $\dfrac{1/12}{3/8} = \dfrac{1}{12} \times \dfrac{8}{3} = \dfrac{8}{36} = \dfrac{2}{9}$.

Step 4: Apply this fraction to the total money earned.
$\text{C's share} = \dfrac{2}{9} \times 2700 = 600$.

Final Answer:
Working from fractions of a single day's job instead of whole-work units, we still land on Rs. 600 for C.
\[ \boxed{600} \]