A mixture of a certain quantity of milk with 16 litres of water is worth 90p…
2023
A mixture of a certain quantity of milk with 16 litres of water is worth 90p per litre. if pure milk be worth Rs.1.08 per litre, how much milk is there in the mixture?
- A.
75
- B.
80
- C.
65
- D.
60
Attempted by 13 students.
Show answer & explanation
Correct answer: B
Solution: Let the quantity of milk be m litres and water be 16 litres.
Set up the price equation for the mixture: (m × 1.08 + 16 × 0) / (m + 16) = 0.90.
Multiply both sides to clear the denominator: 1.08m = 0.90m + 14.4, so 0.18m = 14.4.
Solve for m: m = 14.4 / 0.18 = 80 litres.
Alternative (allegation method): Difference between milk price and mixture price = 1.08 − 0.90 = 0.18; difference between mixture price and water price = 0.90 − 0 = 0.90. So milk:water = 0.90:0.18 = 5:1. With 16 litres of water, milk = 5 × 16 = 80 litres.
Answer: 80 litres.