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P and Q can complete a work in 36 and 12 days respectively. If they work alternate days starting with P, in how many days P and Q can complete the work alternatively?


1. 12 days
2. 16 days
3. 18 days
4. 20 days
5. 26 days

1 Answer

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Best answer
Correct Answer - Option 3 : 18 days

Given:

P can complete the work in 36 days

Q can complete the same work in 12 days

Concept used:

Total work = Efficiency × Time period

Calculation:

Taking the L.C.M of 36 and 12

L.C.M of 36 & 12 = 36

⇒ One day work of P = 36/36 = 1

⇒ One day work of Q = 36/12 = 3

⇒ Work completed in two days = 1 + 3 = 4

⇒ Work completed in one day (Alternatively) = 4/2 = 2

⇒ Number of days to complete the whole work = 36/2 = 18

∴ The number of days to complete the whole work is 18 days.

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