GATE CS 2011 Q65 — General Aptitude

We can solve this problem using the standard formula for repeated dilution/replacement:

$$Q_n = Q_0 \left(1 - \frac{x}{V}\right)^n$$

Where:

• $Q_0$ = Initial quantity of pure spirit = $10$ litres
• $x$ = Quantity of liquid removed and replaced in each step = $1$ litre
• $V$ = Total capacity of the container = $10$ litres
• $n$ = Number of times the replacement process is performed = $3$

Substituting the values into the formula:

$$Q_3 = 10 \left(1 - \frac{1}{10}\right)^3$$

$$Q_3 = 10 \left(\frac{9}{10}\right)^3$$

$$Q_3 = 10 \times 0.729 = 7.29 \text{ litres}$$

Therefore, the amount of spirit left in the container is $7.29$ litres.