A 100-litre solution contains acid and water in the ratio 3:2. Some quantity of this solution is removed and replaced with pure a…

Question

A 100-litre solution contains acid and water in the ratio 3:2. Some quantity of this solution is removed and replaced with pure acid. If the final ratio of acid to water becomes 7:3, how many litres of solution were replaced?

1. A. 35 litres
2. B. 25 litres (Correct answer)
3. C. 50 litres
4. D. 20 litres

Correct Answer

Option B — 25 litres

Detailed Solution & Explanation

The correct answer is 25 litres.

Key Points

• Start with 100 litres in 3 : 2, i.e. 60 L acid and 40 L water.
• Removing x litres of the mixture takes away $0.6x$ acid and $0.4x$ water; the replacement is pure acid, so acid becomes $60 - 0.6x + x$ and water $40 - 0.4x$.
• Setting $\dfrac{60 + 0.4x}{40 - 0.4x} = \dfrac{7}{3}$ gives $180 + 1.2x = 280 - 2.8x$, so $4x = 100$ and x = 25.

Additional Information

• Only the water is lost and never replaced, so tracking water alone is the quicker route: $40 - 0.4x$ must be $\tfrac{3}{10}$ of 100, giving $x = 25$ directly.
• The total volume stays at 100 litres because what is removed is replaced litre for litre — that constant is what makes the shortcut work.
• Check the finished mixture: acid $= 70$ L, water $= 30$ L, and $70 : 30$ does simplify to $7 : 3$ ✓

प्रश्न (हिन्दी में)

100 लीटर के घोल में अम्ल और पानी का अनुपात 3:2 है। इस घोल की कुछ मात्रा निकालकर शुद्ध अम्ल से बदल दी जाती है। यदि अम्ल और पानी का अंतिम अनुपात 7:3 हो जाता है, तो कितने लीटर घोल को बदला गया?

1. A. 35 लीटर
2. B. 25 लीटर
3. C. 50 लीटर
4. D. 20 लीटर