JAMB 2019 Mathematics · Question 54

A man bought a car newly for ₦1,250,000. He had a crash with the car and later sold it at the rate of…

Question

A man bought a car newly for ₦1,250,000. He had a crash with the car and later sold it at the rate of ₦1,085,000. What is the percentage gain or loss of the man?

A.43.7% loss
B.13.2% gain
C.13.2% loss
D.43.7% gain

Answer: C. 13.2% loss

Explanation written with AI and checked against the answer key

Analysis

To solve this problem, we need to determine whether the man made a profit (gain) or incurred a loss.

Cost Price (CP): The amount the man originally paid for the car = ₦1,250,000.
Selling Price (SP): The amount the man sold the car for = ₦1,085,000.

Since the Selling Price is less than the Cost Price, the man incurred a loss.

Concept

The formula for calculating the percentage loss is:

\text{Percentage Loss} = \left( \frac{\text{Loss}}{\text{Cost Price}} \right) \times 100\%

Where:

\text{Loss} = \text{Cost Price} - \text{Selling Price}

Step-by-Step Solution

Step 1: Calculate the actual loss in Naira.

\text{Loss} = 1,250,000 - 1,085,000

\text{Loss} = 165,000

Step 2: Calculate the percentage loss.

\text{Percentage Loss} = \left( \frac{165,000}{1,250,000} \right) \times 100\%

Step 3: Simplify the calculation. Cancel out the zeros:

\text{Percentage Loss} = \left( \frac{165}{1,250} \right) \times 100\%

\text{Percentage Loss} = \frac{165}{12.5}

\text{Percentage Loss} = 13.2\%

Since the selling price was lower than the cost price, this is a 13.2% loss.

Conclusion

Comparing our result to the given options, we find that the correct choice is C.

Exam Tip

Always check if the Selling Price is higher or lower than the Cost Price before calculating. If $SP < CP$ , it is a loss; if $SP > CP$ , it is a gain. This simple check helps you eliminate two of the four options immediately!

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