Question

How much water must be added to 60 litres of milk, costing \rupee20 per litre, to get a mixture worth \rupee10\( \frac{2}{3} \) per litre?

• A. 15 litres
• B. 20 litres
• C. 25 litres
• D. 10 litres

Hint:

In mixture problems, use the formula for the average cost of the mixture: \[ \text{Average cost} = \frac{\text{Cost of first liquid} + \text{Cost of second liquid}}{\text{Total quantity}} \]

Answer 1

The Correct Option is A

Step 1: Let \( x \) litres of water be added to 60 litres of milk. Water is free (cost \rupee0), and milk costs \rupee20/litre. The mixture value is \rupee\( 10 \frac{2}{3} \) or \rupee\( \frac{32}{3} \) per litre. \[ \text{Average price} = \frac{60 \times 20 + x \times 0}{60 + x} = \frac{1200}{60 + x} \] Step 2: Equating to the average cost: \[ \frac{1200}{60 + x} = \frac{32}{3} \Rightarrow 1200 \times 3 = 32(60 + x) \Rightarrow 3600 = 1920 + 32x \Rightarrow 32x = 1680 \Rightarrow x = \frac{1680}{32} = 15 \] Thus, 15 litres of water must be added.