Question

Anish and Bala can do a work in 8 days, Bala and Cynthia can do the same work in 12 days. Anish, Bala, and Cynthia together can finish it in 6 days. How many days will Anish and Cynthia together do it?

• A. 4 days
• B. 6 days
• C. 8 days
• D. 12 days

Hint:

Subtraction of rate equations helps isolate the individual or combined rates, making it easier to solve complex work sharing problems.

Answer 1

The Correct Option is C

Step 1: Find the combined work rate of all pairs and the trio.
Let \( \frac{1}{A} \), \( \frac{1}{B} \), and \( \frac{1}{C} \) represent the work rates of Anish, Bala, and Cynthia respectively.

\[ \frac{1}{A} + \frac{1}{B} = \frac{1}{8}, \quad \frac{1}{B} + \frac{1}{C} = \frac{1}{12}, \quad \frac{1}{A} + \frac{1}{B} + \frac{1}{C} = \frac{1}{6} \]

Step 2: Isolate and solve for Anish and Cynthia's combined work rate.
Subtract the first two equations from the trio's equation:

\[ \frac{1}{A} + \frac{1}{C} = \frac{1}{6} - \left( \frac{1}{8} - \frac{1}{12} \right) = \frac{1}{8} \]

Days required = \( \frac{1}{\text{combined rate}} = 8 \text{ days} \)