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How many kg of rice at Rs. 54 per kg must be mixed with 30 kg of rice at Rs. 40 per kg, so that on selling the mixture at Rs 48.4 per kg, there will be a profit of 10%?
- A22
- B18
- C15
- D12
Answer not set
Discussion 1
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CCommunity
Let ‘x’ kg of rice at Rs. 54 per kg be mixed
Total weight of mixture = (x + 30) kg
Cost price of (x + 30) kg mixture = 54x + 30 × 40 = 54x + 1200
⇒ Cost price of 1 kg mixture = (54x + 1200)/(x + 30)
Now, when selling price is Rs. 48.4 per kg, profit is 10%
⇒ Cost price of 1 kg mixture + 10% of Cost price = Selling price
⇒ 110% of Cost price of 1 kg mixture = Selling price
⇒ Cost price of 1 kg mixture = 48.4/1.1 = Rs. 44
Hence, we get,
⇒ (54x + 1200)/(x + 30) = 44
⇒ 54x + 1200 = 44x + 1320
⇒ 10x = 120
⇒ x = 120/10 = 12
∴ 12 kg of rice must be added
Total weight of mixture = (x + 30) kg
Cost price of (x + 30) kg mixture = 54x + 30 × 40 = 54x + 1200
⇒ Cost price of 1 kg mixture = (54x + 1200)/(x + 30)
Now, when selling price is Rs. 48.4 per kg, profit is 10%
⇒ Cost price of 1 kg mixture + 10% of Cost price = Selling price
⇒ 110% of Cost price of 1 kg mixture = Selling price
⇒ Cost price of 1 kg mixture = 48.4/1.1 = Rs. 44
Hence, we get,
⇒ (54x + 1200)/(x + 30) = 44
⇒ 54x + 1200 = 44x + 1320
⇒ 10x = 120
⇒ x = 120/10 = 12
∴ 12 kg of rice must be added