Question

The total wages of work is Rs. 25600. A alone can do this piece of work in 8 days and B alone can do it in 12 days. If A and B work on alternate days on this piece of work, then find the share of A.

1. Rs. 8000
2. Rs. 10,000
3. Rs. 16,000
4. Rs. 20,000

Answer 1

Correct Answer - Option 3 : Rs. 16,000

Given:

Total wages = Rs. 25,600

A alone can do a piece of work in = 8 days

B alone can do a piece of work in = 12 days

A and B work on alternate days

Calculation:

Work for 1^st two days = 1/8 + 1/12

⇒ 5/24

∴ Work for 8 days = 5/24 × 8/2

⇒ 5/6

∴ Remaining work = 1 – 5/6

⇒ 1/6

On 9^th day = 1/8

∴ Remaining work after 9 days = 1/6 – 1/8

⇒ 1/24

∴ B will finish this work in = 12 × 1/24

⇒ 1/2 day

Clearly, A worked for 5 days from starting.

∴ work done by A in 5 days = 1/8 × 5

⇒ 5/8

∴ A’s share = 5/8 × 25,600

⇒ 5 × 3200

⇒ Rs. 16,000

∴ A’s share is Rs. 16,000.