Numerical answer
A trader buys 120 kg of rice at ₹40 per kg. He sells one-third of it at a profit of 20% and one-fourth of it at a loss of 10%. At what price (in ₹ per kg) must he sell the remaining rice to make an overall profit of 15%?
Show answer and solution
Answer: 50.4
Total cost = 120 × 40 = ₹4800. Target revenue for 15% profit = 4800 × 1.15 = ₹5520.
- One-third = 40 kg sold at 40 × 1.2 = ₹48/kg → ₹1920.
- One-fourth = 30 kg sold at 40 × 0.9 = ₹36/kg → ₹1080.
Revenue so far = ₹3000. Remaining quantity = 120 − 40 − 30 = 50 kg, which must fetch 5520 − 3000 = ₹2520. Price = 2520 ÷ 50 = ₹50.4 per kg.
Tip: Always convert the overall profit target into a total revenue figure first; then the balance is simply 'target minus what has been realised'.
- One-third = 40 kg sold at 40 × 1.2 = ₹48/kg → ₹1920.
- One-fourth = 30 kg sold at 40 × 0.9 = ₹36/kg → ₹1080.
Revenue so far = ₹3000. Remaining quantity = 120 − 40 − 30 = 50 kg, which must fetch 5520 − 3000 = ₹2520. Price = 2520 ÷ 50 = ₹50.4 per kg.
Tip: Always convert the overall profit target into a total revenue figure first; then the balance is simply 'target minus what has been realised'.
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