Question

A mixture contains 60 litre of milk. x litre of solution is taken out and is replaced by water. This process is repeated two times. If the final quantity of milk is 48.6 litres, then find the value of x.

1. 9 litres
2. 8 litres
3. 7 litres
4. 6 litres
5. None of these

Answer 1

Correct Answer - Option 4 : 6 litres

Given:

Initial concentration = 60 litre

Final concentration = 48.6 litre

Quantity removed in each cycle = x litre

The process is repeated two times means: n = 2

Formula:

FC = IC × (1 – Quantity removed in each cycle/total IC)ⁿ

Here,

FC = final concentration

IC = Initial concentration

n = The process repeated how many times

Calculation:

We know that –

FC = IC × (1 – Quantity removed in each cycle/total IC)ⁿ …….(1)

Put all the given values in equation (1) then we get

48.6 = 60 × (1 – x/60)²

⇒ 48.6/60 = (1 – x/60)²

⇒ (486/600) = (1 – x/60)²

⇒ (81/100)² = (1 – x/60)²

⇒ (9/10)² = (1 – x/60)²

⇒ 9/10 = 1 – x/60

⇒ x/60 = 1 – 9/10

⇒ x/60 = 1/10

⇒ 10x = 60

⇒ x = 60/10

⇒ x = 6

∴ The Value of x = 6 litres