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A, B and C have certain number of chocolates in the ratio of 3 : 2 : 5. If A takes 10 chocolates from B and 20 chocolates from C, the ratio of the chocolates of B and C becomes 1 : 3. What is the total number of chocolates they have initially?

A, B and C have certain number of chocolates in the ratio of 3 : 2 : 5. If A takes 10 chocolates from B and 20 chocolates from C, the ratio of the chocolates of B and C becomes 1 : 3. What is the total number of chocolates they have initially? Correct Answer 100

Given:

The ratio of chocolates of A, B and C is 3 : 2 : 5.

A takes 10 chocolates from B.

A takes 20 chocolates from C.

The ratio of the chocolates of B and C becomes 1 : 3.

Concept Used:

Remaining chocolates = Initial chocolates - Given chocolates to other 

Calculation:

Let the number of chocolates of A, B and C be 3x, 2x and 5x.

A takes 10 chocolates from B.

The remaining chocolates to B = 2x - 10

A takes 20 chocolates from C.

The remaining chocolates to C = 5x - 20

The ratio of the chocolates of B and C is 1 : 3.

⇒ (2x - 10)/(5x - 20) = 1/3

⇒ 6x - 30 = 5x - 20

⇒ x = 10

The total number of chocolates = (3x + 2x + 5x) = 10x = 10 × 10 = 100

∴ The total number of chocolates is 100.

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