Vessel P contains a mixture of milk and water in the ratio of 4 : 3 respectively. 35 liters of this mixture is taken out and poured into Vessel Q, which already contains x liters of milk and 25 liters of water. If the ratio of milk to water in Vessel Q becomes 5 : 4, find the value of
x.

ATQ, Vessel P contains milk and water in the ratio of 4 : 3. Total parts = 4 + 3 = 7 35 liters of mixture is taken out from Vessel P. Quantity of milk in 35 liters mixture = 35 × 4/7 = 20 liters Quantity of water in 35 liters mixture = 35 × 3/7 = 15 liters Now, this mixture is added to Vessel Q. Vessel Q already contains x liters of milk and 25 liters of water. After adding the mixture from Vessel P: Final milk in Vessel Q = x + 20 Final water in Vessel Q = 25 + 15 = 40 liters Given final ratio of milk to water = 5 : 4 So, (x + 20) : 40 = 5 : 4 Now, cross multiply: 4 × (x + 20) = 5 × 40 4x + 80 = 200 4x = 200 − 80 4x = 120 x = 120/4 x = 30