A shopkeeper has 36L of Castor oil and 48L of Groundnut oil. He wants to store both the oils in containers such that each container has the same capacity of oil. How many ways can he do this in?

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Solution

The correct option is C 6
The shopkeeper wants to store oils of capacities 36L and 48L in equal-sized containers.
This is possible if and only if the capacity of each container is a common factor of 36 and 48.

Thus, the number of ways this can be done = the number of common factors of 36 and 48.

Factors of 36 = 1, 2, 3, 4, 9, 12, 18, 36
Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 24, 48

Common factors of 36 and 48 = 1, 2, 3, 4, 6, 12.

⇒ The storing can be done in 6 ways.

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