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    How much water must be added to 60 litres of milk at 112\frac1221​​ litres for Rs. 20 so as to have a mixture worth Rs. 1023\frac2332​​ a litre?
    Question

    How much water must be added to 60 litres of milk at 112\frac12​ litres for Rs. 20 so as to have a mixture worth Rs. 1023\frac23​ a litre?

    A.

    7 litres

    B.

    15 litres

    C.

    9 litres

    D.

    8 litres

    Correct option is B

    Given:

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

    Final mixture value = ₹1023\frac{2}{3} ​= ₹10.666... per litre

    Water has no cost

    Formula Used:

    Water = (CP of milkMean PriceMean PriceCP of water)×Milk\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 = ₹1023\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 = 14×60=15 litres \frac{1}{4} \times 60 = 15 \text{ litres}​​

    Thus, 15 litres of water must be added

    Alternate Solution: 

    Water = 14×60=15 litres \frac{1}{4} \times 60 = 15 \text{ litres}

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