Question

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

• A. 1440
• B. 1176
• C. 1680
• D. 2520

Answer 1

The Correct Option is C

1. Given Quantities

Ankita has:

• 4 kg of cashews
• 14 kg of peanuts
• 6 kg of almonds

Total quantity = \( 4 + 14 + 6 = 24 \) kg

2. Selling Plan

She plans to earn a total profit of ₹1752.

Assume the average cost price of the mixture is \( x \) rupees/kg.

So, marked price = \( x + 73 \) rupees/kg

3. Selling Distribution

Ankita sells:

• 4 kg at full marked price
• 20 kg at a 20% discount

 

Total Selling Price = \[ 4(x + 73) + 0.8 \times 20(x + 73) = 4(x + 73) + 16(x + 73) \] \[ = 20(x + 73) \]

4. Profit Equation

Given total profit is ₹1752:

\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \] \[ 1752 = 20(x + 73) - \text{Cost Price} \] \[ \text{Cost Price} = 20x + 1460 - 1752 = 20x - 292 \]

5. Given Price Ratio

We know:

\[ 7C = 30P = 9A \]

Let all equal ₹630k (a constant multiple), then:

\[ C = \frac{630k}{7} = 90k, \quad P = \frac{630k}{30} = 21k, \quad A = \frac{630k}{9} = 70k \]

6. Total Cost Price in Terms of k

Total cost = \[ 4C + 14P + 6A = 4(90k) + 14(21k) + 6(70k) \] \[ = 360k + 294k + 420k = 1074k \]

Given: Total cost = ₹4296

\[ 1074k = 4296 \Rightarrow k = \frac{4296}{1074} = 4 \]

7. Amount Spent on Almonds

Since \( A = 70k = 70 \times 4 = ₹280 \), and Ankita had 6 kg of almonds: \[ \text{Total almond cost} = 6 \times 280 = ₹1680 \]

Answer: ₹1680

Answer 2

1. Given

Ankita bought:

• 4 kg of Cashews (C)
• 14 kg of Peanuts (P)
• 6 kg of Almonds (A)

The cost ratio is given as:

\[ 7C = 30P = 9A \]

Let: \[ 7C = 30P = 9A = 630k \]

Then, \[ C = 90k,\quad P = 21k,\quad A = 70k \]

2. Cost Price of Total Purchase

\[ \text{Cost Price} = 4C + 14P + 6A \] \[ = 4(90k) + 14(21k) + 6(70k) = 360k + 294k + 420k = 1074k \]

3. Marked Up Price

Profit intended = ₹1752

\[ \text{Marked Price} = \text{Cost Price} + \text{Profit} = 1074k + 1752 \]

4. Selling Price Distribution

She sold:

• \(\frac{1}{6}\) of goods at full price
• \(\frac{5}{6}\) of goods at 20% discount, i.e., at \(\frac{4}{5}\) of marked price

 

Selling Price:

\[ \frac{1}{6}(1074k + 1752) + \frac{4}{5} \cdot \frac{5}{6}(1074k + 1752) = \frac{5}{6}(1074k + 1752) \]

5. Profit Equation

Profit = Selling Price - Cost Price

\[ \frac{5}{6}(1074k + 1752) - 1074k = 744 \]

Compute \(\frac{1074k}{6} = 716\)

\[ \Rightarrow k = \frac{716 \times 6}{1074} = 4 \]

6. Amount Spent on Almonds

\[ \text{Cost of almonds} = 6A = 6 \times 70k = 420k \] \[ \text{Putting } k = 4 \Rightarrow 420 \times 4 = ₹1680 \]

Therefore, the correct answer is: ₹1680