How much water must be added to 60 litres of milk at 1$$\frac12$$​ litres for Rs. 20 so as to have a mixture worth Rs. 10$$\frac23$$​ a litre?

Correct option is B

Given:

60 litres of milk at ₹1.5 per litre = ₹20

Final mixture value = ₹10$$\frac{2}{3}$$​= ₹10.666... per litre

Water has no cost

Formula Used:

Water = $$\left( \frac{\text{CP of milk} - \text{Mean Price}}{\text{Mean Price} - \text{CP of water}} \right) \times \text{Milk}$$​​

Solution:

Cost price of milk = ₹20 for 1.5 litres = ₹20 ÷ 1.5 = ₹13.33/litre

Mean price = ₹10$$\frac{2}{3}$$​ = ₹10.67

Water's cost = ₹0

Using alligation:

Milk : Water  = (10.67 - 0) : (13.33 - 10.67)

= 10.67 : 2.66

= 4 : 1

Water = $$\frac{1}{4} \times 60 = 15 \text{ litres}$$​​

Thus, 15 litres of water must be added

Alternate Solution: ​

Water = $$\frac{1}{4} \times 60 = 15 \text{ litres}$$​