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In a market, the price of medium quality mangoes is half that of good mangoes. A shopkeeper buys 80 kg80 \mathrm{~kg} good mangoes and 40 kg40 \mathrm{~kg} medium quality mangoes from the market and then sells all these at a common price which is 10%10 \% less than the price at which he bought the good ones. His overall profit is

Solution

✅ Correct Option: 2

We need to set up the costs and selling prices clearly.


Let the price of good quality mangoes = gg rupees per kg

Since medium quality mangoes cost half of good mangoes:

Price of medium quality mangoes = g2\tfrac{g}{2} rupees per kg


The shopkeeper buys:

80 kg good mangoes at gg per kg = 80g80g rupees

40 kg medium mangoes at g2\tfrac{g}{2} per kg = 40×g2=20g40 \times \tfrac{g}{2} = 20g rupees

Total cost price = 80g+20g=100g80g + 20g = 100g rupees


The shopkeeper sells ALL mangoes at a common price.

This common selling price = 10% less than the price of good mangoes

= g−0.10g=0.9gg - 0.10g = 0.9g rupees per kg

Total quantity sold = 80 + 40 = 120 kg

Why 120 kg? Because he sells all the mangoes he bought - both good and medium quality together.

Total selling price = 120 kg × 0.9g per kg = 108g108g rupees


Profit = Selling price - Cost price = 108g−100g=8g108g - 100g = 8g rupees

Profit percentage = ProfitCost price×100%\dfrac{\text{Profit}}{\text{Cost price}} \times 100\%

= 8g100g×100%=8%\dfrac{8g}{100g} \times 100\% = 8\%

Therefore, his overall profit is 8%.


In mixed inventory problems like this, always:

Calculate total cost by adding individual costs

Find the common selling price per unit

Multiply by total quantity to get total selling price

Use the profit percentage formula: ProfitCost Price×100%\dfrac{\text{Profit}}{\text{Cost Price}} \times 100\%

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