A dishonest shopkeeper sells sugar at Rs. 18/kg which he has bought at Rs. 15/kg and he is giving 800 gm instead of 1000 gm. Find his actual profit percentage.

Question: A dishonest shopkeeper sells sugar at Rs. 18/kg which he has bought at Rs. 15/kg and he is giving 800 gm instead of 1000 gm. Find his actual profit percentage.

• 10%
• 25%
• 50% 
• 75%

Answer: 

shortcut formula :

$$\text{Profit \%}=\left(\frac{\text{Extra gain}+\text{False weight loss}}{\text{False weight loss}}\right)\times 100$$

• Extra gain per kg = Selling Price – Cost Price = $18 - 15 = 3$

• False weight loss = $\frac{1000 - 800}{800}$

applying the formula:

$$\text{Profit \%} = \left( \frac{3 + 15 \times \frac{200}{800}}{12} \right) \times 100$$ $$= \left( \frac{3 + 3}{12} \right) \times 100$$ $$=\left(\frac{6}{12}\right)\times 100=50\mathrm{\%}$$

**The actual profit percentage is 50%.

Additional Method :

• Cost Price (CP) per kg = Rs. 15

• Selling Price (SP) per kg = Rs. 18

• Actual weight given = 800 gm instead of 1000 gm

*Find the Cost Price of 800 gm

Since the cost price of 1 kg (1000 gm) is Rs. 15, the cost price of 800 gm is:

$$\text{CP of 800 gm} = \left( \frac{800}{1000} \right) \times 15 = \frac{8}{10} \times 15 = Rs. 12$$

* Find the Profit

• The dishonest shopkeeper sells 800 gm at Rs. 18.

• His cost price for 800 gm is Rs. 12.

• Profit per 800 gm = Selling Price – Cost Price = Rs. 18 - Rs. 12 = Rs. 6.

* Find the Profit Percentage

$$\text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100$$ $$= \left( \frac{6}{12} \right) \times 100 = 50\%$$

**The actual profit percentage of the shopkeeper is 50%.

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