An oil of Rs.42 per kg is mixed with 10 kg oil of Rs.69 per kg. If price of…
2025
An oil of Rs.42 per kg is mixed with 10 kg oil of Rs.69 per kg. If price of mixture oil is Rs.60 per kg then what is the quantity of first type of oil in the mixture?
- A.
6 kg
- B.
5 kg
- C.
8 kg
- D.
4 kg
Attempted by 1 students.
Show answer & explanation
Correct answer: B
Rule of alligation: when two ingredients of different prices are mixed to get a mixture of a given mean price, the ratio in which they are mixed is the inverse of the differences of their prices from the mean price — ratio of (cheaper oil's quantity) : (dearer oil's quantity) = (dearer price − mean price) : (mean price − cheaper price).
Let the required quantity of the cheaper oil (Rs.42 per kg) be x kg. The dearer oil (Rs.69 per kg) is given as 10 kg, and the mean price of the mixture is Rs.60 per kg.
By the rule of alligation, ratio of quantities = (dearer price − mean price) : (mean price − cheaper price) = (69 − 60) : (60 − 42) = 9 : 18 = 1 : 2.
This ratio is (quantity of cheaper oil) : (quantity of dearer oil) = x : 10, so x : 10 = 1 : 2.
Cross-multiplying, 2x = 10, so x = 5.
Substituting x = 5 back into the weighted-average price: (42 × 5 + 69 × 10) ÷ (5 + 10) = (210 + 690) ÷ 15 = 900 ÷ 15 = Rs.60 per kg, which matches the given mixture price, confirming the quantity of the first (cheaper) oil is 5 kg.