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In a mixture the ratio of brandy and whisky is 5 ∶ 3. If 12 ml of mixture is taken out and 5 ml of whisky is added to the mixture, such that the ratio of brandy and whisky becomes 35 ∶ 31. What is the concentration of brandy in the mixture at the beginning?

In a mixture the ratio of brandy and whisky is 5 ∶ 3. If 12 ml of mixture is taken out and 5 ml of whisky is added to the mixture, such that the ratio of brandy and whisky becomes 35 ∶ 31. What is the concentration of brandy in the mixture at the beginning? Correct Answer 25 ml

Let the quantity of brandy and whisky in the mixture be 5x and 3x respectively

12 ml mixture is taken out

The quantity of mixture taken out is removed in the same ratio as the concentration of contents in the mixture

Quantity of beer left after removal = 5x – (12 × 5/8) = 5x – 7.5

Quantity of whisky left after removal = 3x – (12 × 3/8) = 3x – 4.5

Now, 5 ml of whisky is added to the mixture, such that the ratio of brandy and whisky becomes 35 ∶ 31

∴ According to question,

(5x – 7.5)/(3x – 4.5 + 5) = 35/31

⇒ 155x – 232.5 = 105x + 17.5

⇒ 50x = 250

⇒ x = 5

∴ Quantity of beer initially = 5 × 5 = 25 ml

Quantity of whisky initially = 3 × 5 = 15 ml

∴ The concentration of brandy in the mixture at the beginning is 25 ml

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