Multiple choice

8 litres of wine are drawn and replaced with water from a cask full of pure wine and the operation is repeated three more times. If the ratio of wine and water left in the cask are now 16:65, how much wine was originally held by the cask? 8 लीटर वाइन निकाली जाती है और शुद्ध शराब से भरे एक पीपे से पानी के साथ प्रतिस्थापित किया जाता है और प्रक्रिया को तीन बार दोहराया जाता है। यदि पीपे में बचे हुए शराब और पानी का अनुपात अब 16:65 है, तो मूल रूप से पीपे में कितनी शराब थी?

  1. 18 litres 18 लीटर

  2. 24 litres 24 लीटर

  3. 32 litres 32 लीटर

  4. 42 litres 42 लीटर

  5. 21 litres 21 लीटर

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

Let initial wine = x litres. After 4 operations of removing 8L and replacing with water, wine left = x(1 - 8/x)^4. Wine:water = 16:65 means wine is 16/81 of total. So x(1 - 8/x)^4 = 16x/81. Solving gives (1 - 8/x)^4 = 16/81, so 1 - 8/x = 2/3, giving x = 24. B is correct.