A man marks his goods 40% above the CP and gives a discount of 10%, What percent profit does he make

Question: A man marks his goods 40% above the CP and gives a discount of 10%, What percent profit does he make ?

• 15 %
• 20 %
• 24 %
• 26 %

Answer: 

$$\text{Profit \%}=(M-D-\frac{M\times D}{100})$$

• M = Mark-up percentage (40%)
• D = Discount percentage (10%)

Substituting values:

$$\text{Profit \%} = \left( 40 - 10 - \frac{40 \times 10}{100} \right)$$ $$= \left( 40 - 10 - 4 \right)$$ $$=26\mathrm{\%}$$

·°· Profit = 26%

Detail Solution:

Given:

• The man marks his goods 40% above the Cost Price (CP).
  • So, Marked Price (MP) = 140% of CP = 1.4 × CP
• He gives a discount of 10% on the Marked Price (MP).
  • So, Selling Price (SP) = 90% of MP = 0.9 × MP

Calculation:

$$SP = 0.9 \times 1.4 \times CP$$ $$SP = 1.26 \times CP$$

Profit %:

$$\text{Profit} = SP - CP = (1.26 \times CP) - CP = 0.26 \times CP$$ $$\text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \times 100 \right)$$ $$= \left( \frac{0.26 \times CP}{CP} \times 100 \right)$$ $$= 26\%$$

·°· The man makes a 26% profit

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