Container P contains a mixture of milk and water in the ratio 7 : 3 respectively. Container Q contains a mixture of milk, water and sugar in the ratio 6 : 5 : 4 respectively. When the mixtures from both containers are combined, the final quantities of milk and water are 118 liters and 70 liters respectively. Find the quantity of sugar in the final mixture.

ATQ, In Container P, milk and water are in the ratio 7 : 3. Let the quantities of milk and water in Container P be 7a and 3a. In Container Q, milk, water and sugar are in the ratio 6 : 5 : 4. Let the quantities of milk, water and sugar in Container Q be 6b, 5b and 4b. Final quantity of milk = 118 liters. So, 7a + 6b = 118 Final quantity of water = 70 liters. So, 3a + 5b = 70 From 3a + 5b = 70: a = (70 − 5b)/3 Put this in 7a + 6b = 118: 7 × (70 − 5b)/3 + 6b = 118 Multiply both sides by 3: 7(70 − 5b) + 18b = 354 490 − 35b + 18b = 354 490 − 17b = 354 17b = 490 − 354 17b = 136 b = 136/17 b = 8 Quantity of sugar in final mixture = 4b Sugar = 4 × 8 = 32 liters