A container originally contains 10 litres of pure spirit. From this container 1 litre of spirit is replaced with 1 litre of water. Subsequently, 1 litre of the mixture is again replaced with 1 litre of water and this process is repeated one more time. How much spirit is now left in the container?

Select one answerSingle correct

Pick an option to check

Solution

Step-by-step verified solution

Official answer: D) 7.29 litres

Quantitative Aptitude

Initial volume of pure spirit, $V = 10\text{ litres}$ . Volume replaced each time, $x = 1\text{ litre}$ . Total number of replacement operations, $n = 3$ (initial replacement, subsequently once, and repeated one more time).

The formula for the quantity of pure liquid remaining after $n$ successive operations is:

\text{Remaining spirit} = V \left(1 - \frac{x}{V}\right)^n

Substitute the values:

\text{Remaining spirit} = 10 \left(1 - \frac{1}{10}\right)^3 = 10 \times (0.9)^3 = 10 \times 0.729 = 7.29\text{ litres}

Hence, the correct option is (D).

Try the question first, then check your work.

Think the official key or this write-up is wrong?

Report error or challenge

Examiner trap

The misconception this question tests

This Quantitative Aptitude previous year question is Q65 of the GATE CSE 2011 paper. Find more GATE CSE PYQs on Quantitative Aptitude in General Aptitude, or browse all GATE CSE PYQs.

Free diagnostic

Where do you stand for GATE?

Take the 20-minute diagnostic: the 3 topics that cost you the most marks, and a rank range. Or sit 5 related Quantitative Aptitude PYQs now with no account.

One GATE CSE PYQ every morning

An official question by email at 7 AM IST, with a link to its verified solution. Unsubscribe in one click.

Quantitative Aptitude in GATE CSE

Quantitative Aptitude has 53 GATE CSE PYQs across 13 papers from 2011 to 2026. 27 of them are 2-mark MCQs like this one, and GATE CSE 2011 has 4.

How GATE tests Quantitative Aptitude

More from GATE CSE 2011

Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.