Question

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

Accepted Answer

C. Let cost of 1 kg cashews $= C$, 1 kg peanuts $= P$, 1 kg almonds $= A$. Given: $7C = 30P = 9A = 630x$ (LCM of 7, 30, 9 is 630). Then: - $C = 90x$ - $P = 21x$ - $A = 70x$ Total quantity of mixture $= 4 + 14 + 6 = 24$ kg. Total Cost Price (CP) $= 4C + 14P + 6A = 4(90x) + 14(21x) + 6(70x) = 360x + 294x + 420x = 1074x$. Let Marked Price per kg be $M$. Marking to make ₹1752 profit on 24 kg: $$24M - 1074x = 1752 \implies 24M = 1074x + 1752$$ $$M = \frac{1074x + 1752}{24}$$ Actual Selling Price (SP): - 4 kg at $M$ - 20 kg at $0.8M$ Total SP $= 4M + 20(0.8M) = 4M + 16M = 20M$. Actual Profit $= 20M - 1074x = 744$. Substitute $20M = 744 + 1074x$, so $M = \frac{744 + 1074x}{20}$. Equating both expressions for $M$: $$\frac{1074x + 1752}{24} = \frac{744 + 1074x}{20}$$ $$5(1074x + 1752) = 6(744 + 1074x)$$ $$5370x + 8760 = 4464 + 6444x$$ $$1074x = 4296 \implies x = 4$$ Amount spent in buying almonds $=

Cost of Almonds in Nut Mixture

Explanation

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