Question

A can do a piece of work in x days and B can do the work in 3x days. To finish the work together, they take 12 days. What is the value of x?

• A. 8
• B. 10
• C. 12
• D. 16

Hint:

For combined work problems, add individual work rates and equate to the combined rate.

Answer 1

The Correct Option is D

Step 1: Work rates
- A’s rate = \(\frac{1}{x}\) work per day
- B’s rate = \(\frac{1}{3x}\) work per day
Step 2: Combined rate
\[ \frac{1}{x} + \frac{1}{3x} = \frac{1}{12} \] \[ \frac{3 + 1}{3x} = \frac{1}{12} \] \[ \frac{4}{3x} = \frac{1}{12} \] Step 3: Solve for \(x\)
Cross multiply:
\[ 4 \times 12 = 3x \] \[ 48 = 3x \] \[ x = 16 \] Thus, Option (D) 16 is correct.