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 purchased at different rates: ₹800, ₹500, and ₹300 per kilogram. The quantities purchased are in the ratio 2 : 3 : 5.

To simplify calculations, we scale this ratio to a total that is a multiple of 6 (since part of the tea, 5 kg, is sold separately). Multiplying the original ratio by 3 gives us:

Quantities: \( 2 \times 3 = 6 \) kg, \( 3 \times 3 = 9 \) kg, \( 5 \times 3 = 15 \) kg 

Total Quantity: \( 6 + 9 + 15 = 30 \) kg

Total Cost:
\( 800 \times 6 = ₹4800 \)
\( 500 \times 9 = ₹4500 \)
\( 300 \times 15 = ₹4500 \)
Total Cost = ₹4800 + ₹4500 + ₹4500 = ₹13,800

A profit of 50% is made on the total cost. Hence,

Profit = \( \frac{50}{100} \times 13,800 = ₹6,900 \)

Total Selling Price = Cost Price + Profit = \( 13,800 + 6,900 = ₹20,700 \)

5 kg of the tea is sold at ₹700 per kg:
\( 5 \times 700 = ₹3,500 \)

Remaining Quantity = \( 30 - 5 = 25 \) kg
Remaining Selling Price = \( 20,700 - 3,500 = ₹17,200 \)

Selling Price per kg of remaining tea =
\( \frac{17,200}{25} = ₹688 \)

Final Answer: ₹688 per kg