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Question
A shopkeeper has 36kg of Besan flour and 24kg of Rice flour. He wants to store both in containers such that each container has the same quantity of flour. In how many ways can he do this?
A shopkeeper has 36kg of Besan flour and 24kg of Rice flour. He wants to store both in containers such that each container has the same quantity of flour. In how many ways can he do this?
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Solution
The correct option is C 6
The shopkeeper wants to store flours of weights 36kg and 24kg in equal-sized containers.
This is possible if and only if the weight of each container is a common factor of 36 and 24.
Thus, the number of ways this can be done = the number of common factors of 36 and 24.
Factors of 36 = 1, 2, 3, 4, 9, 12, 18, 36
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
Common factors of 36 and 24 = 1, 2, 3, 4, 6, 12.
Thus the storage can be done in 6 ways.
The shopkeeper wants to store flours of weights 36kg and 24kg in equal-sized containers.
This is possible if and only if the weight of each container is a common factor of 36 and 24.
Thus, the number of ways this can be done = the number of common factors of 36 and 24.
Factors of 36 = 1, 2, 3, 4, 9, 12, 18, 36
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
Common factors of 36 and 24 = 1, 2, 3, 4, 6, 12.
Thus the storage can be done in 6 ways.
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