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A dishonest shopkeeper sells his grocery at celling price and earns a profit equal to 20% of his selling price. If he uses false weight to make this gain, find the weight lose per kilogram that lead to the profit if he sold 25 Kg of goods at Rs. 20 per kilogram.
  • a)
    100 g
  • b)
    150 g
  • c)
    200 g
  • d)
    250 g
  • e)
    300 g
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A dishonest shopkeeper sells his grocery at celling price and earns a...
Given:
- Selling price of grocery = Ceiling price
- Profit earned = 20% of the selling price
- Quantity sold = 25 kg
- Selling price per kg = Rs. 20

To Find:
The weight loss per kilogram that leads to the profit.

Solution:

Step 1: Calculate the profit earned per kilogram.
Profit earned = 20% of the selling price
Let's assume the cost price per kilogram = Rs. x

Profit per kilogram = Selling price per kilogram - Cost price per kilogram
20% of selling price per kilogram = Rs. 20 - x

Step 2: Calculate the total profit earned.
Total selling price = Selling price per kilogram * Quantity sold
Total selling price = Rs. 20 * 25 = Rs. 500

Total cost price = Cost price per kilogram * Quantity sold
Total cost price = x * 25

Total profit = Total selling price - Total cost price
Total profit = Rs. 500 - 25x

Since the dishonest shopkeeper sells at the ceiling price, the profit earned is equal to the total profit.

Step 3: Calculate the weight loss per kilogram.
Weight loss per kilogram = (Total profit) / (Profit per kilogram)
Weight loss per kilogram = (500 - 25x) / (20 - x)

We need to find the weight loss per kilogram that leads to the profit. Therefore, we need to find the value of x that satisfies the equation.

Step 4: Solve for x.
Weight loss per kilogram = (500 - 25x) / (20 - x) = 200 g
Multiplying both sides by (20 - x):
500 - 25x = 200(20 - x)
500 - 25x = 4000 - 200x
175x = 3500
x = 20

Step 5: Calculate the weight loss per kilogram.
Weight loss per kilogram = (500 - 25x) / (20 - x)
Weight loss per kilogram = (500 - 500) / (20 - 20)
Weight loss per kilogram = 0 / 0
Weight loss per kilogram is undefined.

Conclusion:
The weight loss per kilogram that leads to the profit is undefined. Therefore, option 'C' (200 g) is incorrect.
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Community Answer
A dishonest shopkeeper sells his grocery at celling price and earns a...
By selling 25 Kg shopkeeper gains 20%
Total cost price = 25 × 20
Total cost price = Rs. 500
The profit obtained on selling 25 Kg = 20% of 500
⇒ The profit obtained on selling 25 kg = Rs. 100
That means profit in weight corresponding to profit in money = Profit / cost price
⇒ Profit in weight = 100 / 20
⇒ Profit in terms of weight = 5 Kg
That is, out of 25 Kg weight, the shopkeeper actually uses only 20 Kg.
The loss per kilogram = 5 / 25
⇒ Loss of weight per kilogram = 1 / 5 kg
⇒ Loss of weight per kilogram = 200g
∴ The weight shopkeeper reduces to get a 20% gain on selling 25kg is 200g per kilogram weight.
Hence, the correct option is (C).
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A dishonest shopkeeper sells his grocery at celling price and earns a profit equal to 20% of his selling price. If he uses false weight to make this gain, find the weight lose per kilogram that lead to the profit if he sold 25 Kg of goods at Rs. 20 per kilogram.a)100 gb)150 gc)200 gd)250 ge)300 gCorrect answer is option 'C'. Can you explain this answer?
Question Description
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