Question

If 'A' and 'B' can do a piece of work in 8 days, while 'A' alone can do it in 12 days. In how many days can 'B' alone do the same work?

• A. 24 days
• B. 12 days
• C. 16 days
• D. 20 days

Hint:

To find the work done by one worker when two workers' combined work rate is given, use: \[ \text{Work rate of B} = \text{Work rate of A and B together} - \text{Work rate of A} \]

Answer 1

The Correct Option is A

Given: - A and B together complete the work in 8 days. - A alone completes the work in 12 days. Step 1: Work done per day by A: \[ \frac{1}{12} \] Step 2: Work done per day by A and B together: \[ \frac{1}{8} \] Step 3: Work done per day by B: \[ \frac{1}{8} - \frac{1}{12} \] Taking LCM of 8 and 12, which is 24: \[ \frac{3}{24} - \frac{2}{24} = \frac{1}{24} \]
Thus, B alone takes 24 days to complete the work.