What percent above should a dealer marks his goods so that after giving a discount of 20%, he will get 20%

Question: What percent above should a dealer marks his goods so that after giving a discount of 20%, he will get 20% ?

Answer: 

 Formula:

$$\text{Markup }\mathrm{\%}=\left(\frac{\text{Profit }\mathrm{\%}+\text{Discount }\mathrm{\%}+(\text{Profit}\mathrm{\%}\times \text{Discount}\mathrm{\%})\mathrm{/}100}{1-(\text{Discount }\mathrm{\%}\mathrm{/}100)}\right)$$

• Profit % = 20

• Discount % = 20

 Calculation:

 $$\text{Markup } \% = \left( \frac{20 + 20 + (20 \times 20) / 100}{1 - (20 / 100)} \right)$$ $$= \left( \frac{20 + 20 + 4}{0.8} \right)$$ $$= \left( \frac{44}{0.8} \right)$$ $$=55\mathrm{\%}$$

*** The dealer should mark the goods 55% above the cost price to gain a 20% profit after a 20% discount.

Detail solution:

Let,  the cost price of the goods be ₹100.

Step 1: 

The dealer gives a 20% discount, so the selling price (SP) is:

 SP=MP−20% of MP=x−20100×x=0.8xSP = MP - 20\% \text{ of } MP = x - \frac{20}{100} \times x = 0.8x

Step 2: 

Since the cost price is ₹100, the selling price should be:

 SP=CP+20% of CP=100+20100×100=120SP = CP + 20\% \text{ of } CP = 100 + \frac{20}{100} \times 100 = 120

So,

$$0.8x = 120$$

Step 3: 

$$x = \frac{120}{0.8} = 150$$

Step 4: 

 $$\text{Percentage increase} = \frac{MP - CP}{CP} \times 100$$ $$= \frac{150 - 100}{100} \times 100 = 50\%$$

** The dealer should mark his goods 50% above the cost price.

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