Ankita buys 4 kg cashews, 14 kg peanuts and 6 kg almonds when the cost of 7 kg cashews is the same as that of 30 kg peanuts or 9 kg almonds. She mixes all the three nuts and marks a price for the mixture in order to make a profit of ₹1752. She sells 4 kg of the mixture at this marked price and the remaining at a 20% discount on the marked price, thus making a total profit of ₹744. Then the amount, in rupees, that she had spent in buying almonds is
Explanation:
Let the price of a kg of peanuts, cashews and almonds is Rs. p, c and a. Given, 7c = 30p = 9a ⇒ c : p : a = 90 : 21 : 70
Ankita mixes 4 kg cashews, 14 kg peanuts and 6 kg almonds, i.e., total 24 kgs. Total cost price of the mixture = 4 × 90x + 14 × 21x + 6 × 70x = 1074x. Cost price/kg = 44.75x/kg
She plans to sells this 24 kg mixture for a Profit of Rs. 1752 i.e, at a profit of 1752/24 = Rs. 73/kg.
She sells 4 kg of this mixture at the original selling price and hence earns a profit of 4 × 73 = Rs. 292.
Total profit she actually earns is Rs. 744.
⇒ Profit earned on remaining 20 kgs = 744 – 292 = Rs. 452. ⇒ Profit originally planned on remaining 20 kgs = 20 × 73 = Rs. 1460.
Cost of this 20 kg = 20 × 44.75x = 895x
⇒ (895x + 1460) × 0.8 = 895x + 452 ⇒ 1460 × 0.8 – 452 = 895x × 0.2 ⇒ 716 = 179x ⇒ x = 4
∴ Price of 6 kg of almonds = 6 × 70 × 4 = 1680
Hence, option (b).
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