Question

A shopkeeper marks up the price by 25% and then gives a discount of 20%. If Cost price is Rs. 800, find the Selling Price.

• A. 780
• B. 820
• C. 840
• D. 800

Hint:

A 25% increase followed by a 20% decrease (or vice-versa) always results in a net change of 0%. This is a useful shortcut to remember as 1.25 \(\times\) 0.80 = 1.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We are given the Cost Price (CP) of an item. The price is first increased (marked up) and then decreased (discounted). We need to find the final Selling Price (SP).
Step 2: Key Formula or Approach:
1. Calculate the Marked Price (MP) after the markup. MP = CP \(\times\) (1 + Markup %).
2. Calculate the Selling Price (SP) after the discount. SP = MP \(\times\) (1 - Discount %).
Alternatively, we can use the formula for successive percentage change: Net Change % = x + y + (xy/100).
Step 3: Detailed Explanation:
Method 1: Step-by-Step Calculation
Given Cost Price (CP) = Rs. 800.
Markup: The price is marked up by 25%.
Markup amount = 25% of 800 = 0.25 \(\times\) 800 = Rs. 200.
Marked Price (MP) = CP + Markup amount = 800 + 200 = Rs. 1000.
Discount: A discount of 20% is given on the Marked Price.
Discount amount = 20% of 1000 = 0.20 \(\times\) 1000 = Rs. 200.
Selling Price (SP) = MP - Discount amount = 1000 - 200 = Rs. 800.
Method 2: Successive Percentage Change
First change (markup) = +25%.
Second change (discount) = -20%.
Net percentage change = \(25 + (-20) + \frac{25 \times (-20)}{100}\)%
= \(5 + \frac{-500}{100}\)%
= \(5 - 5\)% = 0%.
A 0% net change means the final price is the same as the initial price.
Selling Price (SP) = Cost Price (CP) = Rs. 800.
Step 4: Final Answer:
The final Selling Price is Rs. 800.