Question

A fruit seller sold 4 kg of oranges at Rs. 120 and incurred a loss of 25%. So, he decided to mark up the price of the remaining fruits. He made a total revenue of Rs. 1000 and an overall profit of 25%. What markup is made on the remaining fruits and the total quantity sold?
Options (Markup, Quantity): (37.5, 40), (40, 20), (20, 25), (25, 32.75)

Hint:

In complex profit/loss problems, always calculate the fundamental cost price first. The CP per unit is usually constant and is the key to linking different parts of the transaction.

Answer 1

Step 1: Understanding the Concept:
This is a multi-stage profit and loss problem. We must first analyze the initial transaction to find the cost price per kg. Then, use the overall profit and revenue information to find the total cost price and the quantity of remaining fruits. Finally, we can calculate the markup on the remaining fruits.
Step 2: Analyze the Initial Sale
The phrase "sold 4 kg of oranges at Rs. 120" implies the total selling price for the 4 kg was Rs. 120.


Selling Price (SP) of first 4 kg = Rs. 120
Loss = 25%
The relationship between SP, Cost Price (CP), and Loss is \(SP = CP \times (1 - \text{Loss Percentage})\). \[ 120 = CP_{4kg} \times (1 - 0.25) = CP_{4kg} \times 0.75 \] \[ CP_{4kg} = \frac{120}{0.75} = \frac{120}{3/4} = 120 \times \frac{4}{3} = 160 \] The cost price of the first 4 kg of oranges was Rs. 160. The cost price per kg is \( \frac{160}{4} = \text{Rs. } 40 \text{ per kg} \).
Step 3: Analyze the Overall Transaction


Total Revenue (Total SP) = Rs. 1000
Overall Profit = 25%
Using the formula \(SP = CP \times (1 + \text{Profit Percentage})\): \[ 1000 = \text{Total CP} \times (1 + 0.25) = \text{Total CP} \times 1.25 \] \[ \text{Total CP} = \frac{1000}{1.25} = \frac{1000}{5/4} = 1000 \times \frac{4}{5} = 800 \] The total cost of all oranges was Rs. 800.
Step 4: Find Total Quantity and Markup on Remaining Fruits
Total CP is Rs. 800, and the CP per kg is Rs. 40. \[ \text{Total Quantity Sold} = \frac{\text{Total CP}}{\text{CP per kg}} = \frac{800}{40} = 20 \text{ kg} \] This answers the second part of the question.
Now, let's find the markup on the remaining fruits.

Quantity of remaining fruits = Total Quantity - Initial Quantity = \(20 - 4 = 16\) kg.
SP of remaining fruits = Total SP - Initial SP = \(1000 - 120 = \text{Rs. } 880\).
New SP per kg (for remaining fruits) = \( \frac{880}{16} = \text{Rs. } 55 \text{ per kg} \).
The CP per kg is still Rs. 40.
Markup Percentage is calculated on the cost price: \[ \text{Markup %} = \frac{\text{New SP} - \text{CP}}{\text{CP}} \times 100 = \frac{55 - 40}{40} \times 100 \] \[ \text{Markup %} = \frac{15}{40} \times 100 = \frac{3}{8} \times 100 = 37.5% \] Step 5: Final Answer
The markup on the remaining fruits is 37.5%, and the total quantity sold is 20 kg.