1440
1176
1680
2520
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.
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
A furniture trader deals in tables and chairs. He has Rs. 75,000 to invest and a space to store at most 60 items. A table costs him Rs. 1,500 and a chair costs him Rs. 1,000. The trader earns a profit of Rs. 400 and Rs. 250 on a table and chair, respectively. Assuming that he can sell all the items that he can buy, which of the following is/are true for the above problem:
(A) Let the trader buy \( x \) tables and \( y \) chairs. Let \( Z \) denote the total profit. Thus, the mathematical formulation of the given problem is:
\[ Z = 400x + 250y, \]
subject to constraints:
\[ x + y \leq 60, \quad 3x + 2y \leq 150, \quad x \geq 0, \quad y \geq 0. \]
(B) The corner points of the feasible region are (0, 0), (50, 0), (30, 30), and (0, 60).
(C) Maximum profit is Rs. 19,500 when trader purchases 60 chairs only.
(D) Maximum profit is Rs. 20,000 when trader purchases 50 tables only.
Choose the correct answer from the options given below: