X purchased a car at Rs.1,50,000 and then sold it to Y at a profit of 5%. Y later sold it back to X at a loss of 2%. Find the overall profit or loss for X in the entire transaction

Correct option is A

Given:

Initial purchase price of the car by X = Rs. 1,50,000

Profit percentage when X sold to Y = 5%

Loss percentage when Y sold back to X = 2%

Solution:

Selling price when X sold to Y:

​$$\text{Selling Price to Y} = \text{Initial Price} \times \left(1 + \frac{\text{Profit \%}}{100}\right)$$​​

​$$= 150000 \times \left(1 + \frac{5}{100}\right) = 150000 \times 1.05 = Rs. 157500$$​​

Repurchase price when Y sold back to X:

$$\text{Repurchase Price from Y} = \text{Selling Price to Y} \times \left(1 - \frac{\text{Loss \%}}{100}\right)$$​​

​$$= 157500 \times \left(1 - \frac{2}{100}\right) = 157500 \times 0.98 = Rs. 154350$$​​

Overall profit or loss for X:

​$$\text{Overall } = \text{Repurchase Price from Y} - \text{Initial Price} \\ = 157500 -154350 = Rs. 3150$$​​

Therefore, X made an overall Profit of Rs. 3150.0 in the transaction.     

Confusion Point: ​

After selling the car to Y on profit, X has 157500 , now to buy back X has to pay from the money he has ,

thus to get overall profit we subtract = 157500 - 154350 = 3150