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A bottle of capacity 80 litres contains alcohol and spirit in the ratio 7 ∶ 3. How much spirit must be added to the mixture, so that the ratio of alcohol and spirit become 2 ∶ 1?
1. 1 litres
2. 2 litres
3. 3 litres
4. 4 litres

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Correct Answer - Option 4 : 4 litres

Given:

The capacity of bottle = 80 litres

Initially, the ratio of alcohol and spirit is 7 ∶ 3

In addition, to spirit, the ratio become 2 ∶ 1

Calculation:

Quantity of alcohol in bottle = \(80 × {7 \ \over 10}\)= 56 liters

Quantity of spirit in bottle = 80 - 56 = 24 liters

Now, let 'x' litres of the spirit be added

∴ \( {56 \ \over 24\; + \;x} = {2 \ \over 1}\)

⇒ 56 = 2 × (24 + x)

⇒ 56 = 48 + 2x

⇒ 2x = 8

⇒ x = 4

∴ 4 liters of spirit is added.

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