Question

To do a certain work, A and B work on alternate days with B beginning the work on the first day. A alone can complete the same work in 24 days. If the work gets completed in \(11 \frac{1}{3}\) days, then B alone can complete \(\rm \frac{7}{9}^{th}\) part of the original work in:
1. 4 days
2. 6 days
3. \(5 \frac{1}{2}\) days
4. \(4 \frac{1}{2}\) days

Answer 1

Correct Answer - Option 2 : 6 days

Given:

Time taken by A to finish a task alone = 24 days 

Calculation:

Let the total work be = 1 

A alone can finish the task in 24 days 

⇒ A's one-day work = 1/24 

A and B complete the whole task in = \(11 \frac{1}{3}\) days 

A and B work on alternate days, with B beginning so, we can say B will work only 6 days 

⇒ A will work only \(11 \frac{1}{3}\) - 6 = \(5 \frac{1}{3}\) days 

If A's one day work = 1/24 of work A completes in 1 day

⇒ A's \(5 \frac{1}{3}\) days work = 1/24 × \(5 \frac{1}{3}\) = 1/24 × 16/3 

⇒ 2/9 

Remaining work = 1 - 2/9 = 7/9 

∴ B does the 7/9th part of the work in 6 days. 

Note-

B, A, B, A, B, A, B, A, B, A, B, A/3

B completely 6-day work

That's why we have taken the 6 days work by B alone.