Question

How much percent above the cost price should a shopkeeper mark his goods so that after allowing a discount $20\%$ on the marked price, he gains$12\%$?

Answer 1

Step 1: Find the Selling Price (SP) of the product:

Given: Gain $=12\%$and the discount $=20\%$

Let the cost price (CP) be $100$

$$\begin{gathered} \mathrm{Gain}=12\%\mathrm{of}100[\mathrm{Gain}=\mathrm{Gain}\%\mathrm{of}\mathrm{CP}] \\ \mathrm{Gain}=\frac{12}{100}\times 100 \\ \mathrm{Gain}=12 \end{gathered}$$

Selling Price of the product

$$\begin{gathered} \mathrm{SP}=100+12[\mathrm{SP}=\mathrm{CP}+\mathrm{Gain}] \\ \mathrm{SP}=112 \end{gathered}$$

Step 2: Find Marked Price (MP):

Let Marked Price (MP) be x

Discount $=\frac{20}{100}\times \mathrm{x}[\mathrm{Discount}=20\%\mathrm{of}\mathrm{MP}]$

Discount $=\frac{1}{5}\mathrm{x}$

$$\begin{gathered} \mathrm{x}-\frac{1}{5}\mathrm{x}=112[\mathrm{MP}-\mathrm{Discount}=\mathrm{SP}] \\ \frac{5\mathrm{x}-\mathrm{x}}{5}=112 \\ \frac{4\mathrm{x}}{5}=112 \\ \mathrm{x}=112\times \frac{5}{4} \\ \mathrm{x}=140 \end{gathered}$$

Marked Price(MP) $=140\mathrm{Rs}$

Step 3: Find the percentage of MP above the CP:

Amount of MP above CP $=MP-CP$

$$\begin{gathered} =140-100 \\ =40\mathrm{Rs} \end{gathered}$$

$$\begin{gathered} \mathrm{Percentage}=\frac{\mathrm{Amount}\mathrm{increased}}{\mathrm{CP}}\times 100 \\ \mathrm{Percentage}=\frac{40}{100}\times 100 \\ =40\% \end{gathered}$$

Hence, the amount of percentage of MP above the CP is $=40\%$.