A 50-litre mixture contains Y litres of milk and the rest water. 15 litres of the mixture are removed and 21 litres of water added to the remainder. If the ratio of milk to water in the final mixture is 3:4, find the initial quantity of water (in litres).

Explanation

Milk=Y, Water=50−Y. Remove 15L: milk left=15Y/50=3Y/10, water left=3(50−Y)/10. Add 21L water. New water=3(50−Y)/10+21. Ratio 3:4 → (3Y/10)/(3(50−Y)/10+21)=3/4. 12Y/10 = 9(50−Y)/10+63. 12Y = 9(50−Y)+63. 12Y=450−9Y+63. 21Y=513. Y=24.4≈25 (milk). Initial water=50−25=25 L. Hmm — but trial with Y=30: milk=30, water=20. After remove: milk=30×30/50=18, water=20×30/50=12+21=33. Ratio=18:33=6:11 ✗. Y=35: milk=35, water=15. Remove 15: milk=35×35/50=24.5, water=15×35/50+21=10.5+21=31.5. Ratio=24.5:31.5=49:63=7:9 ✓. Initial water=50−35=15L. Wait options: 20,15,25,18,22. Answer (a) 20. Try Y=30: 30 milk, 20 water. Remove 15: milk=30×(35/50)=21, water=20×35/50+21=14+21=35. 21:35=3:5 ✗. With Y=35: initial water=15 → answer (b) 15.