In what ratio must tea of Rs.42 per kg be mixed with tea of Rs.50 per kg so…
2025
In what ratio must tea of Rs.42 per kg be mixed with tea of Rs.50 per kg so that cost of mixture is Rs.45 per kg?
- A.
5:3
- B.
3:5
- C.
2:3
- D.
3:4
Show answer & explanation
Correct answer: A
Alligation Rule: When two ingredients of different prices are mixed to get a mixture of a given mean price, the ratio of the quantity of the cheaper ingredient to the quantity of the dearer ingredient equals (Dearer price − Mean price) : (Mean price − Cheaper price).
Let the cheaper tea cost C = Rs.42/kg, the dearer tea cost D = Rs.50/kg, and the required mean price M = Rs.45/kg.
Compute the dearer-side difference: D − M = 50 − 45 = 5.
Compute the cheaper-side difference: M − C = 45 − 42 = 3.
By the alligation rule, quantity of cheaper tea : quantity of dearer tea = (D − M) : (M − C) = 5 : 3.
Cross-check by weighted average: mixing 5 parts of the Rs.42/kg tea with 3 parts of the Rs.50/kg tea gives (5×42 + 3×50) / 8 = (210 + 150) / 8 = 360 / 8 = Rs.45/kg, exactly the required mean price — confirming the ratio.
So the two teas must be mixed in the ratio 5 : 3.
