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A mixture has two liquids A and B in a certain ratio. When 10 litres of B is added to the mixture, the ratio of A and B becomes 13 : 9. When 30 litres of B is added to the mixture, the ratio of A and B becomes 1 : 1. Find the initial ratio.

A mixture has two liquids A and B in a certain ratio. When 10 litres of B is added to the mixture, the ratio of A and B becomes 13 : 9. When 30 litres of B is added to the mixture, the ratio of A and B becomes 1 : 1. Find the initial ratio. Correct Answer 13 : 7

GIVEN :

After adding 10 litres of B is added to the mixture, the ratio of A and B becomes 13 : 9

After adding 30 more litres of B is added to the mixture, the ratio of A and B becomes 1 : 1

 

FORMULA USED :

Basic concept of mixture and Alligation.

 

ASSUMPTION :

Let the volumes of A and B be a and b respectively.

 

CALCULATION :

a/(b + 10) = 13/9

⇒ 9a = 13b + 130

⇒ a/(b + 30) = 1

⇒ a = b + 30

Putting the value of a in the equation, we get

⇒ 9(b + 30) = 13b + 130

⇒ 9b + 270 = 13b + 130

⇒ 140 = 4b

⇒ b = 35

⇒ a = b + 30 = 65

∴ the initial ratio was 65 : 35 = 13 : 7

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