Question

From a jar of wine containing 32 litres, 4 litres is drawn out, and the jar is filled up with water. If the same proportion of wine is further drawn out two more times, what proportion of wine to water will be there in the resulting mixture?
1. 245 : 166
2. 343 : 169
3. 363 : 173
4. 323 : 189

Answer 1

Correct Answer - Option 2 : 343 : 169

Calculation:

Amount of wine left in the jar = total quantity initially in the jar × [1 - (amount of wine replaced with water in each draw)/total quantity]^{(number of times the process repeated)}

Amount of wine left in the jar = 32 × [1 - (4/32)]³ = 32 × (7/8)³

Amount of wine left in the jar = 32 × (343/512)

Then, amount of water in the jar = 32 × (512 - 343)/512 = 32 × 169/512

Ratio of wine to water in the final mixture = 32 × (343/512) : 32 × 169/512 = 343 : 169

∴ The ratio of wine to water in the final mixture is 343 : 169.