Arithmetic

Profit & Loss

Hard

Ankita buys $4 \mathrm{~kg}$ cashews, $14 \mathrm{~kg}$ peanuts and $6 \mathrm{~kg}$ almonds when the cost of $7 \mathrm{~kg}$ cashews is the same as that of $30 \mathrm{~kg}$ peanuts or $9 \mathrm{~kg}$ almonds. She mixes all the three nuts and marks a price for the mixture in order to make a profit of Rs.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 Rs. 744. Then the amount, in rupees, that she had spent in buying almonds is

$1176$

$1680$

$2520$

$1440$

✅ Correct Option: 2

We need to set up relationships between the costs and work through the profit scenarios systematically.

Let us define variables for the cost per kg:

Cashews = $C$ rupees per kg

Peanuts = $P$ rupees per kg

Almonds = $A$ rupees per kg

From the given information: 7 kg cashews = 30 kg peanuts = 9 kg almonds (same cost)

To make calculations easier, let us set this common cost equal to some value. We'll use $630x$ (this choice will make the individual costs come out as nice round numbers).

So: $7C = 30P = 9A = 630x$

From this:

$C = 630x ÷ 7 = 90x$ rupees per kg

$P = 630x ÷ 30 = 21x$ rupees per kg

$A = 630x ÷ 9 = 70x$ rupees per kg

Ankita buys:

4 kg cashews at $90x$ each = $360x$ rupees

14 kg peanuts at $21x$ each = $294x$ rupees

6 kg almonds at $70x$ each = $420x$ rupees

Total cost price = $360x + 294x + 420x = 1074x$ rupees

Total weight of mixture = $4 + 14 + 6 = 24$ kg

Let the marked price be $y$ rupees per kg.

Scenario 1: If she sold all 24 kg at marked price $y$

Total selling price = $24y$

Profit = $24y - 1074x = 1752$ rupees ... (1)

Scenario 2: What actually happened

4 kg sold at marked price $y = 4y$ rupees

Remaining 20 kg sold at 20% discount = $20 × (0.8y) = 16y$ rupees

Total selling price = $4y + 16y = 20y$ rupees

Actual profit = $20y - 1074x = 744$ rupees ... (2)

Subtracting equation (2) from equation (1):

$(24y - 1074x) - (20y - 1074x) = 1752 - 744$

$4y = 1008$

$y = 252$ rupees per kg

Substituting back into equation (2):

$20(252) - 1074x = 744$

$5040 - 1074x = 744$

$1074x = 4296$

$x = 4$

Amount spent on almonds = 6 kg × $70x$ rupees per kg

= $420x$ rupees

= $420 × 4$

= $1680$ rupees

The key insight here is setting up two profit scenarios - the intended profit vs. actual profit - and using the difference to find the marked price. Once we have that, we can work backwards to find the cost structure.

Answer: 1680 rupees

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