Question

A man and a boy working together can complete a work in 24 days. If for the last 6 days, the man alone does the work, then it is completed in 26 days. How long will the boy take to complete the work alone?

• A. \(72\) days
• B. \(64\) days
• C. \(84\) days
• D. \(24\) days
• E. \(32\) days

Answer 1

The Correct Option is A

Concept: This is a
time and work problem:

• Work rate = Work per day
• Total work = sum of individual contributions

Step 1: Let total work = 1 unit.
\[ \text{Man + Boy rate} = \frac{1}{24} \]
Step 2: Work distribution.

• First 20 days: both work
• Last 6 days: only man works

\[ \text{Work in 20 days} = \frac{20}{24} = \frac{5}{6} \] Remaining work: \[ 1 - \frac{5}{6} = \frac{1}{6} \]
Step 3: Find man's rate.
\[ 6 \times \text{Man's rate} = \frac{1}{6} \Rightarrow \text{Man's rate} = \frac{1}{36} \]
Step 4: Find boy's rate.
\[ \text{Boy's rate} = \frac{1}{24} - \frac{1}{36} \] \[ = \frac{3 - 2}{72} = \frac{1}{72} \]
Step 5: Time taken by boy alone.
\[ \text{Time} = 72 \text{ days} \]
Step 6: Option analysis.

• (A) 72: Correct \checkmark
• (B) 64: Incorrect $\times$
• (C) 84: Incorrect $\times$
• (D) 24: Combined time $\times$
• (E) 32: Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (A).