In what ratio metal A at Rs.68 per kg be mixed with another metal at Rs.96 per…
2025
In what ratio metal A at Rs.68 per kg be mixed with another metal at Rs.96 per kg so that cost of alloy (mixture) is Rs.78 per kg?
- A.
5:8
- B.
4:7
- C.
3:7
- D.
9:5
Attempted by 1 students.
Show answer & explanation
Correct answer: D
Concept
The Rule of Alligation states: when two ingredients priced differently are mixed to form a blend of a given mean price, the ratio in which they must be mixed equals the ratio of the differences between each price and the mean price, taken crosswise — Quantity of cheaper ingredient : Quantity of dearer ingredient = (Price of dearer − Mean price) : (Mean price − Price of cheaper).
Application
Let the cost price of the cheaper metal be CP1 = Rs. 68 per kg, the cost price of the dearer metal be CP2 = Rs. 96 per kg, and the mean price of the mixture be M = Rs. 78 per kg.
Compute the difference between the dearer price and the mean price: CP2 − M = 96 − 78 = 18.
Compute the difference between the mean price and the cheaper price: M − CP1 = 78 − 68 = 10.
By the Rule of Alligation, Quantity of metal at Rs. 68 per kg : Quantity of metal at Rs. 96 per kg = 18 : 10.
Simplify 18:10 by dividing both terms by their greatest common divisor, 2, giving the ratio 9 : 5.
Cross-check
Take 9 parts of the Rs. 68 metal and 5 parts of the Rs. 96 metal (14 parts total). Total cost = (9 × 68) + (5 × 96) = 612 + 480 = 1092. Mean price = 1092 ÷ 14 = Rs. 78 per kg, which matches the given mean price of Rs. 78/kg — confirming the ratio 9 : 5 is correct.
