Question

A container ‘A’ contains a mixture of two solutions P and Q in the ratio of 3 : 5. If 24 litres of mixture is taken out and replaced with same quantity of solution Q, then final ratio of two solution in the container ‘A’ is 1 : 3. What is the quantity of solution container hold ?

1. 56 litres
2. 68 litres
3. 72 litres
4. 65 litres
5. 75 litres

Answer 1

Correct Answer - Option 3 : 72 litres

Given:

A container ‘A’ contains a mixture of two solutions P and Q in the ratio of 3 : 5.

Concept Used:

The resultant mixture = Initial solution - taken out solution + added solution (if given)

Calculation:

A container ‘A’ contains a mixture of two solutions P and Q in the ratio of 3 : 5.

Let the total quantity of mixture in container ‘A’ be 8x.

According to the question:

24 litres of mixture is taken out

The quantity of solution P is taken out = (3/8) × 24 = 9

The quantity of solution Q is taken out = (5/8) × 24 = 15

The final ratio of two solution in the container ‘A’ is 1 : 3.

⇒ (3x - 9)/(5x - 15 + 24) = 1/3

⇒ (3x - 9)/(5x + 9) = 1/3

⇒ 9x - 27 = 5x + 9

⇒ 4x = 36

⇒ x = 9

The quantity of of mixture in container ‘A’ = 8 × 9 = 72

∴ The quantity of of mixture in container ‘A’ is 72 litres.