Question

There are two jars. One contains 8 litres of brandy, second contains 8 litres of water. One litre of brandy is transferred from first jar to second jar. Again one litre of mixture is taken out from jar second and transferred to jar 1. Ratio of the amount of water in first jar to the amount of brandy in second jar is

• A. 6 : 7
• B. 7 : 6
• C. 1 : 1
• D. 8 : 9

Hint:

There are two jars. One contains 8 litres of brandy, second contains 8 litres of water. One litre of brandy is transferred from first jar to second jar. Again one litre of mixture is taken out from jar second and transferred to jar 1. Ratio of the amount of water in first jar to the amount of brandy in second jar is

Answer 1

The Correct Option is C

Initial State: Jar 1: 8L Brandy (B), 0L Water (W). Jar 2: 0L B, 8L W. Step 1: Transfer 1L B from Jar 1 to Jar 2. Jar 1: 7L B, 0L W (Total 7L). Jar 2: 1L B, 8L W (Total 9L). Step 2: Transfer 1L mixture from Jar 2 to Jar 1. Mixture in Jar 2: \(\frac{1}{9}\) B, \(\frac{8}{9}\) W concentration. Amount transferred: \(\frac{1}{9}\)L B, \(\frac{8}{9}\)L W. Final State: Jar 1: B = \(7 - \frac{1}{9} = \frac{62}{9}\) L. W = \(0 + \frac{8}{9} = \frac{8}{9}\) L. Jar 2: B = \(1 - \frac{1}{9} = \frac{8}{9}\)L. W = \(8 - \frac{8}{9} = \frac{64}{9}\)L. Ratio Required: (Water in Jar 1) : (Brandy in Jar 2) = \(\frac{8}{9}\) : \(\frac{8}{9}\) = 1:1. This matches option (3).