Average, Mixture and Alligation Question 6 - CAT 2021
A person buys tea of three different qualities at ₹ 800, ₹ 500, and ₹ 300 per kg, respectively, and the amounts bought are in the proportion 2 : 3 : 5. She mixes all the tea and sells one-sixth of the mixture at ₹ 700 per kg. The price, in INR per kg, at which she should sell the remaining tea, to make an overall profit of 50%, is:
Step-by-Step Explanation
Choose a convenient total weight based on the given blending proportion ratio (2 : 3 : 5).
Let the amounts bought be 12 kg, 18 kg, and 30 kg (Total pool = 60 kg).
(This scale factor ensures that the 1 / 6 fraction step yields a clean integer value)
- Calculate the total Cost Price (CP):
Total CP = 12 × 800 + 18 × 500 + 30 × 300 = 9600 + 9000 + 9000 = ₹27600
- Determine the required total Revenue for a 50% profit:
Targeted Revenue = 27600 × 1.50 = ₹41400
- Track the revenue earned from sales:
First Sale: 1 / 6 of the mixture (10 kg) is sold at ₹700/kg:
Revenue₁ = 10 × 700 = ₹7000
- Remaining Target:
Balance Revenue Needed = 41400 − 7000 = ₹34400
The remaining quantity to sell is 60 − 10 = 50 kg.
Required Price per kg = 34400 / 50 = ₹688
Correct Option: B
💡 FundaMakers Tip:
When handling mixture pricing with fractional sales, select a smart common multiple for the total weight early on. This keeps your scratchpad work focused on straightforward multiplication rather than dragging fractions along, preventing arithmetic errors.