Ankita buys 4kg cashews, 14kg peanuts, and 6kg almonds when the cost of 7kg cashews is the same as that of 30kg peanuts or 9kg almonds. She mixes all three nuts and marks a price for the mixture in order to make a profit of ₹1752. She sells 4kg 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 buying almonds is
1440
1176
1680
2520
The Correct Option is C
Approach Solution - 1
Given Information:
Ankita had 4kg cashews, 14kg peanuts, and 6kg almonds.
She planned to make a total profit of ₹1752 by selling these nuts.
2. Average Buying Price:
Let's assume the average buying price of these nuts is "x" rupees per kg.
3. Marked Price and Selling:
Ankita planned to make a profit of ₹73 on these 24kgs of nuts.
So, the marked price of these 24kgs of nuts is ₹(x+73) per kg.
4. Selling Calculation:
She sells 4 kg of the mixture at the marked price of ₹(x+73) per kg.
She sells the remaining 20kg at a 20% discount on the marked price, which is 0.8 times the marked price.
Total selling price = \(4(x+73)+0.8\times20(x + 73)\)
5. Profit Calculation:
Total Profit = Selling Price - Cost Price
₹1752=\([4(x+73)+0.8\times20(x+73)]\)- Cost Price
6. Calculating Cost Price:
Solve the above equation for Cost Price:
₹1752=4x+292+16x+1160-Cost Price
Cost Price=4x+292+16x+1160-₹1752
Cost Price=20x-300
7.Using Given Information about Costs:
We are given that the cost of 7kg cashews is the same as the cost of 30kg peanuts or 9kg almonds:
7C=30P=9A
8. Solving for Costs:
Let 7C=30P=9A=630k (k is a constant)
C=90k, P=21k, A=70k
9. Calculating Total Cost:
The buying price of 4kg cashews, 14kg peanuts, and 6kg almonds is:
Total Cost=4C+14P+6A
Total Cost=4(90k)+14(21k)+6(70k)
Total Cost=360k+294k+420k=1074k
10. Calculating k:
We know that the total cost is ₹4296:
1074k=4296
k=4
11. Calculating Amount Spent on Almonds:
The cost of almonds is A=70k=280
Amount Spent on Almonds=6A=\(6\times280\) = ₹1680
So, the amount Ankita had spent on buying almonds is ₹1680.
Approach Solution -2
Given :
Ankita bought 4C, 14P and 6A
7C = 30P = 9A
Let's assume that 7C = 30P = 9A = 630k
Now , C = 90k, P = 21k, and A = 70k
Cost price of 4C, 14P and 6A :
4(90k) + 14(21k) + 6(70k) = 1074k
Marked up price is 1074k + 1752
Selling price = \(\frac{1}{6}(1074k+1752)+(\frac{4}{5})(\frac{5}{6})(1074k+1752)\)
\(=\frac{5}{6}(1074k+1752)\)
Profit = Selling Price - Cost Price
\(1460-\frac{1074k}{6}=744\)
\(\frac{1074k}{6}=716\)
Therefore, k = 4
Now , money spent on buying almonds :
420k = 420 × 4
= 1680rs
Therefore, the correct option is (A) : 1680
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