Maths Question: Matthew Bought Two Cars. He Sold Both the Cars for $45,000…

Last year, Matthew bought two cars. This year, he sold both the cars for $45,000 each. On one, he earned 20% profit, and on the other, he made a 20% loss. What was his net profit or loss?

The options are A. Profit of $7,500, B. Loss of $3,750, C. Profit of $3,750 and D. Loss of $7,500. Can you attempt this question? Solve and compare your answer to the solution below.

SOLUTION TO THE QUESTION

In business and accounting, net income is a measure of the profitability of a venture. It is an entity’s income minus the cost of goods sold, expenses, depreciation and amortization, interest, and taxes for an accounting period.

Now, Let the first car be called Car 1 and the second Car be called Car 2.

Analyzing Car 1 (20% profit)

We don’t know the cost of car 1. so, let it be x

20% profit is ²⁰„_{100 times} x

ˆ´ x + ²⁰„₁₀₀ x = $45,000
finding the lcm and cross multiplying
100x + 20x = $45,000 x 100
120x = $4500000

x = ^4500000„₁₂₀ = $37,500
Therefore, cost price for Car 1 = $37,500

Analyzing Car 2 (20% loss)

We don’t know the cost of car 2. so, let it be x

20% profit is ²⁰„_{100 times} x

ˆ´ x – ²⁰„₁₀₀ x = $45,000
finding the lcm and cross multiplying
100x – 20x = $45,000 x 100
80x = $4500000

x = ^4500000„8₀ = $56,250
Therefore, cost price for Car 2 = $56,250

Profit/Loss= Selling Price -Cost Price
Tota Selling Price = $45000 + $45000 =$90,000
Total Cost Price = $37,500 + $56,250 = $93,750

Profit/Loss= $90,000 – $93,750 = $-3,750. THE ANSWER IS OPTION B

The cost price is higher than selling price, therefore, there is a loss of $3,750

Car 1 Profit: Selling price – cost price = $45,000 – $37,500 = $7,500
Car 2 Loss:  Selling price – cost price = $45,000 –  $56,250 = $11,250

Hope yo understand?