Question

Three workers A, B C can together complete a piece of work in 8 days. A takes 8 days less than B to complete the same work alone. If A can complete the work alone in 16 days, then the number of days in which C alone can complete the work

• A. 48
• B. 52
• C. 56
• D. 64

Hint:

Always convert "days to complete" into "rate of work" (1/days) before performing addition or subtraction.

Answer 1

The Correct Option is A

Concept: This is a work-done problem. The combined work rate of multiple workers is the sum of their individual rates.

Step 1: Determine the work rate of A and B.
A completes the work in 16 days. \[ \text{Rate of A} = \frac{1}{16} \text{ work/day} \] A takes 8 days less than B, meaning B takes \( 16 + 8 = 24 \) days. \[ \text{Rate of B} = \frac{1}{24} \text{ work/day} \]

Step 2: Determine the combined rate of A, B, and C.
Given they complete it in 8 days together: \[ \text{Rate (A+B+C)} = \frac{1}{8} \text{ work/day} \]

Step 3: Calculate the rate of C.
\[ \text{Rate of C} = \text{Rate (A+B+C)} - (\text{Rate of A} + \text{Rate of B}) \] \[ \text{Rate of C} = \frac{1}{8} - \left( \frac{1}{16} + \frac{1}{24} \right) \] \[ \text{Rate of C} = \frac{1}{8} - \frac{5}{48} = \frac{6 - 5}{48} = \frac{1}{48} \]

Step 4: Calculate the days taken by C.
Since the rate of C is \( \frac{1}{48} \), C takes 48 days to complete the work alone. \centerline{{48}}