Question

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

• A. 692
• B. 688
• C. 653
• D. 675

Answer 1

The Correct Option is B

Three types of tea are bought at different prices: ₹ 800, ₹ 500, and ₹ 300 per kilogram. They're bought in a ratio of 2 : 3 : 5. But since the total ratio isn't a multiple of 6, we adjust it to 6 : 9 : 15, making calculations easier.
The total cost is found by multiplying each price by the corresponding quantity and adding them together: ₹ 800 × 6 + ₹ 500 × 9 + ₹ 300 × 15 = ₹ 13,800.
With a 50% profit, the profit amount is half of the cost, making it ₹ 6,900. So, the selling price is the cost plus profit: ₹ 13,800 + ₹ 6,900 = ₹ 20,700.
For 5 kilograms sold at ₹ 700 per kilogram, the selling price is ₹ 3,500. Subtracting this from the total selling price gives ₹ 17,200, which is for the remaining 25 kilograms.
To find the selling price per kilogram for the remaining tea, divide ₹ 17,200 by 25, 
so, giving ₹ 688 per kilogram.