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Vessels P and Q contains mixture of Alcohol and water. The amount of Alcohol in vessel P and Q is (a – 6)% and (a + 12)% respectively. If both mixtures are mixed together in a certain ratio to get 90 litres of mixture in which the amount of Alcohol is (a + 5)%, what was the amount of mixture used from vessel Q.

Vessels P and Q contains mixture of Alcohol and water. The amount of Alcohol in vessel P and Q is (a – 6)% and (a + 12)% respectively. If both mixtures are mixed together in a certain ratio to get 90 litres of mixture in which the amount of Alcohol is (a + 5)%, what was the amount of mixture used from vessel Q. Correct Answer 55 liters 

Given

Amount of Alcohol in vessel P and Q respectively = (a – 6)% and (a + 12)%

Amount of Alcohol in 90 liters mixture = (a + 5)%

Formula used

Quantity of cheaper/Quantity of dearer = (Price of dearer - Mean price)/(Mean price - Price of cheaper)

Calculation

Applying Allegation formula

⇒ (a + 12) – (a + 5)/(a + 5) – (a – 6)

⇒ (a + 12 – a – 5)/(a + 5 – a + 6)

⇒ 7/11

Now the amount mixture of vessel Q is used = 11/(7 + 11) × 90

⇒ 55 liters

∴ The amount mixture used from vessel Q is 55 liters.

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