Question:medium

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

Updated On: Jan 15, 2026

  • 1440

  • 1176

  • 1680

  • 2520

Show Solution

The Correct Option is C

Solution and Explanation

1. Initial Quantities

Ankita possesses:

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

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

2. Profit Objective

Target profit is ₹1752.

Let the average cost per kg of the mixture be \( x \) rupees.

The marked price is set at \( x + 73 \) rupees/kg.

3. Sales Strategy

Ankita sells:

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

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

4. Profit Calculation

Total profit recorded is ₹1752:

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

5. Cost Ratio Identification

The price ratio is given as:

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

Equating all to a constant \( 630k \), we get:

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

6. Total Cost Derivation

The total cost is calculated as:

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

It is provided that the Total cost = ₹4296.

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

7. Expenditure on Almonds

The value of \( A \) is \( 70k = 70 \times 4 = ₹280 \) per kg. With 6 kg of almonds, the total cost is: \[ \text{Total almond cost} = 6 \times 280 = ₹1680 \]

Answer: ₹1680

Was this answer helpful?
0

Top Questions on Profit and Loss

Questions Asked in CAT exam

The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.
View Solution