Question

The milk and water in a mixture are in the ratio 7:5. When 15 litres of water is added to it, the ratio of milk and water in the new mixture becomes 7:8. The total quantity of water in the new mixture is:

• A. 30 litres
• B. 60 litres
• C. 48 litres
• D. 40 litres

Hint:

When mixing substances in a given ratio, use algebraic expressions to represent the quantities and solve using cross-multiplication.

Answer 1

The Correct Option is D

Let the initial quantity of milk be \( 7x \) and the initial quantity of water be \( 5x \), where \( x \) is the common multiple. After 15 litres of water is added, the new quantity of water becomes \( 5x + 15 \). The new ratio of milk to water is given as 7:8, so: \[ \frac{7x}{5x + 15} = \frac{7}{8} \] Now, cross-multiply to solve for \( x \): \[ 8 \times 7x = 7 \times (5x + 15) \] \[ 56x = 35x + 105 \] \[ 56x - 35x = 105 \] \[ 21x = 105 \] \[ x = 5 \] Now, substitute \( x = 5 \) into the expressions for the quantity of water: \[ \text{Initial water} = 5x = 5 \times 5 = 25 \, \text{litres} \] \[ \text{Final water} = 25 + 15 = 40 \, \text{litres} \] Thus, the total quantity of water in the new mixture is 40 litres.