A shopkeeper fixes the marked price of an item \( 35 \% \) above its cost price. The percentage of discount allowed to gain \( 8 \% \) is.
Let the cost price (CP) of the item be ₹100 (for easy calculation).
The marked price (MP) is 35% above the cost price, so:
\[
MP = 100 + 35\% \text{ of } 100 = 100 + 35 = ₹135
\]
The shopkeeper wants to gain 8%, so the selling price (SP) should be:
\[
SP = 100 + 8\% \text{ of } 100 = 100 + 8 = ₹108
\]
Now, let the discount percentage be x%. The selling price is calculated as:
\[
SP = MP \times \left(1 - \frac{x}{100}\right)
\]
Substituting values:
\[
108 = 135 \times \left(1 - \frac{x}{100}\right)
\]
Solving for x:
\[
\frac{108}{135} = 1 - \frac{x}{100}
\]
\[
0.8 = 1 - \frac{x}{100}
\]
\[
\frac{x}{100} = 1 - 0.8 = 0.2
\]
\[
x = 20\%
\]
The required discount percentage is 20%.
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