Numerical answer
A trader buys 120 kg of rice at ₹40 per kg. He sells 40% of it at a profit of 20% and 35% of it at a loss of 10%. At what price (in ₹ per kg) must he sell the remaining rice so that his overall profit is 12%?
Show answer and solution
Answer: 52
Total cost = 120 × 40 = ₹4,800. Required revenue for a 12% profit = 4,800 × 1.12 = ₹5,376.
- 40% of 120 = 48 kg sold at 40 × 1.2 = ₹48/kg → ₹2,304
- 35% of 120 = 42 kg sold at 40 × 0.9 = ₹36/kg → ₹1,512
Revenue so far = ₹3,816. Remaining quantity = 120 − 48 − 42 = 30 kg, which must bring in 5,376 − 3,816 = ₹1,560.
Price = 1,560 ÷ 30 = ₹52 per kg.
Tip: Work with total revenue targets rather than trying to average percentages across unequal quantities.
- 40% of 120 = 48 kg sold at 40 × 1.2 = ₹48/kg → ₹2,304
- 35% of 120 = 42 kg sold at 40 × 0.9 = ₹36/kg → ₹1,512
Revenue so far = ₹3,816. Remaining quantity = 120 − 48 − 42 = 30 kg, which must bring in 5,376 − 3,816 = ₹1,560.
Price = 1,560 ÷ 30 = ₹52 per kg.
Tip: Work with total revenue targets rather than trying to average percentages across unequal quantities.
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