Question

How much water should be added to 60 liters of milk at a price of $1\frac12$ per liter for ₹20 to get the mixture at a price of ₹ $10\frac23$?

• A. 7 litres
• B. 15 litres
• C. 9 litres
• D. 8 litres

Answer 1

Answer:

B. 15 litres

The milk costs $₹20$ for $1\frac12$ litres (which is $\frac{3}{2}$ litres).

Price of milk per litre$= \frac{\text{Total Cost}}{\text{Quantity}}$

$= \frac{20 \text{ per litre}}{\frac{3}{2}}$

$= 20 \times \frac{2}{3} = \frac{40}{3}$

You have 60 litres of milk. The total cost of the milk, which will be the total cost of the final mixture (since water is assumed to be free), is:

Total Cost $= \text{Quantity of Milk} \times \text{Price per Litre}$

$= 60 \text{ litres} \times\frac{40}{3}$

$= 20 \times 40 = 800$

The final mixture is required to be worth ₹$10\frac23$ a litre.

$\text{Desired Price per Litre} = 10\frac23 = \frac{32}{3}$

The total quantity of the mixture is calculated by dividing the total cost by the desired price per litre:

$\text{Total Quantity of Mixture} = \frac{\text{Total Cost}}{\text{Desired Price per Litre}} = \frac{800}{\frac{32}{3}} = 800 \times \frac{3}{32}$

$\text{Total Quantity of Mixture} = \frac{800 \times 3}{32} = \frac{(25 \times 32) \times 3}{32} = 25 \times 3 = \mathbf{75 \text{ litres}}$

The total quantity of the mixture is the sum of the milk and the added water.

$\text{Water Added} = \text{Total Quantity of Mixture} - \text{Quantity of Milk}$

$\text{Water Added} = 75 \text{ litres} - 60 \text{ litres} = \mathbf{15 \text{ litres}}$