A container originally contains 10 litres of pure spirit. From this container,…
2011
A container originally contains 10 litres of pure spirit. From this container, 1 litre of spirit 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?
Answer: D. 7.29 litres — Key idea: when 1 litre is removed from 10 litres, the fraction of spirit remaining is 9/10. Repeating the process multiplies this factor each time.…
- A.
7.58 litres
- B.
7.84 litres
- C.
7 litres
- D.
7.29 litres
Attempted by 57 students.
Show answer & explanation
Correct answer: D
Key idea: when 1 litre is removed from 10 litres, the fraction of spirit remaining is 9/10. Repeating the process multiplies this factor each time.
Step-by-step calculation:
After the first replacement: spirit = 10 × (9/10) = 9 litres.
After the second replacement: spirit = 9 × (9/10) = 8.1 litres.
After the third replacement: spirit = 8.1 × (9/10) = 7.29 litres.
Using the compact formula: final amount = 10 × (9/10)^3 = 10 × 0.729 = 7.29 litres.