Question : A and B working separately can do a piece of work in 9 and 15 days respectively. If they work on alternate days, starting with A, then the work will be completed in:
Option 1: 10 days
Option 2: 11 days
Option 3: 9 days
Option 4: 12 days
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Correct Answer: 11 days
Solution :
Given: A and B working separately can do a piece of work in 9 and 15 days respectively. They work on alternate days, starting with A.
Let the total work = LCM of 9 and 15 = 45 units
A’s 1 day work = $\frac{45}{9}$ = 5 units
B’s 1 day work = $\frac{45}{15}$ = 3 units
If they work on alternate days, they will finish (5 + 3) = 8 units of work in 2 days,
In 10 days they will finish (8 × 5) = 40 units of work,
The remaining work = (45 – 40) = 5 units of work, which A can finish on the 11th day.
So, the work will be completed in 11 days.
Hence, the correct answer is 11 days.
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