Multiple choice

The diluted alcohol contains only 7 litres of alcohol and the rest is water. A new mixture whose concentration is 40%, is to be formed by replacing alcohol. How many litres of mixture shall be replaced with pure alcohol if there was initially 28 litres of water in the mixture? अल्कोहल में केवल 7 लीटर शुद्ध अल्कोहल है और शेष पानी है। एक नया मिश्रण जिसकी सांद्रता 40% है, अल्कोहल को प्रतिस्थापित करके बनानी है। यदि मिश्रण में प्रारम्भ में 28 लीटर पानी था तो कितने लीटर मिश्रण को शुद्ध अल्कोहल के साथ प्रतिस्थापित करना चाहिए?

  1. 42/5 L

  2. 35/4 L

  3. 47/8 L

  4. 14/3 L

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial: 7L alcohol + 28L water = 35L total (20% alcohol). Let x L be removed and replaced with pure alcohol. Alcohol removed = 0.2x, remaining alcohol = 7 - 0.2x, water removed = 0.8x, remaining water = 28 - 0.8x. After adding x alcohol: new alcohol = 7 - 0.2x + x = 7 + 0.8x. New total = 35L. Required: (7 + 0.8x)/35 = 0.4, so 7 + 0.8x = 14, hence 0.8x = 7, x = 35/4 = 8.75L. The concentration equation accounts for both removal and replacement.