By selling an umbrella for N2000, a shopkeeper gains 20%. During a clearance sale the shopkeeper allows a discount of 10% on the market price. Find his gain percent during the sale season
Explanation
To determine the gain percent during the sale season, follow these steps:
1. Calculate the Cost Price (CP):
Given that the shopkeeper gains 20% by selling the umbrella for N2000, we first need to find the cost price.
Let \( CP \) be the cost price. The selling price (SP) is N2000, and the gain is 20% of the cost price:
\[
SP = CP + 0.20 \times CP = 1.20 \times CP
\]
\[
2000 = 1.20 \times CP
\]
\[
CP = \frac{2000}{1.20} = \frac{2000 \times 100}{120} = \frac{200000}{120} = 1666.67
\]
2. Calculate the Discounted Selling Price:
During the sale, a 10% discount is given on the market price (SP), which is N2000:
\[
\text{Discounted SP} = SP - 0.10 \times SP = 0.90 \times SP
\]
\[
\text{Discounted SP} = 0.90 \times 2000 = 1800
\]
3. Calculate the Gain During the Sale Season:
The gain during the sale is:
\[
\text{Gain} = \text{Discounted SP} - CP
\]
\[
\text{Gain} = 1800 - 1666.67 = 133.33
\]
To find the gain percent:
\[
\text{Gain Percent} = \left( \frac{\text{Gain}}{CP} \right) \times 100
\]
\[
\text{Gain Percent} = \left( \frac{133.33}{1666.67} \right) \times 100 \approx 8\%
\]
The gain percent during the sale season is 8%.
The correct answer is D. 8%.