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Asha and Bhuvan can do a piece of work in 6 days and 9 days, respectively. They work on alternate days, starting with Asha on
the first day. In how many days will the work be completed?
6 days
7 days
9 days
8 days
- Asha can complete the work in 6 days, so she does 1/6 of the work each day.
- Bhuvan can complete the work in 9 days, so he does 1/9 of the work each day.
- When working alternately, Asha works on the 1st, 3rd, 5th, etc., and Bhuvan on the 2nd, 4th, 6th, etc.
- Add their contributions in two-day cycles:
- Day 1: Asha does 1/6 of the work.
- Day 2: Bhuvan does 1/9 of the work.
- Total for two days: 1/6 + 1/9 = 3/18 + 2/18 = 5/18 of the work.
- After 6 days (3 cycles), they would have completed:
- 3 cycles × 5/18 per cycle = 15/18 of the work.
- On the 7th day, it's Asha's turn.
- She will do another 1/6 of the work.
- 15/18 + 1/6 = 15/18 + 3/18 = 18/18 = 1 (full work).
- So, the work is completed in 7 days.
Answer: Option 2 - 7 days
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