A vessel contains milk and water in the ratio 5:1. If 24 litres of mixture is taken out and then 10 litres of water is added, the new ratio becomes 5:6. Find the initial quantity of the mixture.

ATQ, Let initial milk = 5x litres and initial water = x litres So, initial quantity of mixture = 6x litres Milk in 24 litres taken out = 24 × 5/6 = 20 litres Water in 24 litres taken out = 24 × 1/6 = 4 litres Remaining milk = 5x − 20 Remaining water = x − 4 After adding 10 litres water, water becomes = x − 4 + 10 = x + 6 According to the question, (5x − 20)/(x + 6) = 5/6 6(5x − 20) = 5(x + 6) 30x − 120 = 5x + 30 25x = 150 x = 6 Initial quantity of mixture = 6x = 6 × 6 = 36 litres