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A container contains 72 L spirit. Rakesh wants to dilute it, so he draws out 12 L spirit and replaces it with same quantity of water and repeats this process one more time. What is the ratio of spirit and water in the final mixture and the quantity of spirit in the resultant mixture?

A container contains 72 L spirit. Rakesh wants to dilute it, so he draws out 12 L spirit and replaces it with same quantity of water and repeats this process one more time. What is the ratio of spirit and water in the final mixture and the quantity of spirit in the resultant mixture? Correct Answer 25 : 11, 50 L

Given:

Initial quantity of mixture = 72 L

Quantity of spirit drawn out = 12 L

Quantity of water added = 12 L

Number of time the process is done = 2

Formula Used:

F = I × n

where x → Quantity of spirit drawn out or water added, I → Initial quantity of mixture, F → Final quantity of mixture, n → Number of times the process is done.

Calculations:

Let the final quantity of mixture be y.

The process is done 2 times

⇒ n = 2      ----(1)

The quantity of spirit drawn out = 12 L      ----(2)

Putting (1) and (2) in the formula below, we get

F = I × n

⇒ y = I × 2

⇒ y = I × (5/6) × (5/6)

⇒ y/I = 25/36

Ratio of spirit and water in the resultant mixture = 25 : (36 – 25)

⇒ Ratio of spirit and water in the resultant mixture = 25 : 11

y = 72 × (25/36)     

⇒ y = 50 L

∴ The ratio of spirit and water in the final mixture is 25 : 11 and the quantity of spirit in the resultant mixture is 50 L.

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