In what ratio should tea of ₹130 per kg be mixed with tea of ₹150 per kg so…
2021
In what ratio should tea of ₹130 per kg be mixed with tea of ₹150 per kg so that on selling the mixture at ₹162 per kg there is a profit of 20%?
- A.
2 : 1
- B.
3 : 1
- C.
4 : 1
- D.
5 : 2
Attempted by 35 students.
Show answer & explanation
Correct answer: B
Key calculation: find the required cost price per kg for the mixture.
Step 1: Compute the required cost price per kg to achieve 20% profit when selling at ₹162/kg: 162/1.2 = ₹135
Step 2: Use the allegation (weighted average) method to find the ratio of ₹130 and ₹150 teas that gives mean cost ₹135:
Ratio = (150 − 135) : (135 − 130) = 15 : 5 = 3 : 1
Step 3: Interpretation: Mix 3 parts of the ₹130/kg tea with 1 part of the ₹150/kg tea.
Check: Average cost = (3×130 + 1×150)/4 = (390 + 150)/4 = 540/4 = ₹135, which matches the required cost.
Answer: Mix in the ratio 3 : 1 (₹130 tea : ₹150 tea).