If a cellphone is purchased for Rs. 490 and sold for Rs. 465.50, what is the percentage loss on the transaction?

Introduction / Context:
This question is from percentage and profit loss but appears under the true discount section because it uses similar percentage concepts. The aim is to find the loss percent when a selling price is lower than the cost price. This is a basic but very important skill in aptitude examinations.

Given Data / Assumptions:

• Cost price (CP) of the cellphone = Rs. 490.
• Selling price (SP) of the cellphone = Rs. 465.50.
• We need to compute the loss percent on the cost price.
• Standard profit loss formulas apply.

Concept / Approach:
Loss is defined as CP minus SP when SP is less than CP. The loss percent is given by: Loss percent = (Loss / CP) * 100 We must compute the absolute loss in rupees and then express it as a percentage of the cost price, taking care with decimal handling.

Step-by-Step Solution:
Step 1: Compute the loss. Loss = CP − SP = 490 − 465.50. Step 2: Subtract to get Loss = 24.50. Step 3: Use the formula for loss percent. Loss percent = (24.50 / 490) * 100. Step 4: Compute the fraction 24.50 / 490 = 0.05. Step 5: Convert to percent: 0.05 * 100 = 5%. Thus the loss percent on selling the cellphone is 5 percent.

Verification / Alternative check:
We can cross check by noting that 5 percent of 490 is: 5% of 490 = (5 / 100) * 490 = 24.50. Since this equals the loss amount calculated earlier, the result is confirmed. Also, the selling price is clearly slightly lower than cost price, so the percentage must be a small number, making 5 percent reasonable.

Why Other Options Are Wrong:
Loss percentages of 10, 15, or 20 percent would correspond to losses of 49, 73.50, or 98 respectively, which are much larger than the actual loss of Rs. 24.50. A value such as 2.5 percent would correspond to a loss of only Rs. 12.25, which is too small. Only 5 percent matches the correct loss figure.

Common Pitfalls:
A common error is to divide by the selling price instead of the cost price when calculating the loss percent. Another frequent mistake is mishandling the decimal part in 465.50 or 24.50. Always remember that percentage calculations for profit or loss are based on the cost price, and perform the subtractions with care to avoid decimal errors.

Final Answer:
The loss percentage on the cellphone sale is 5%.