Question

A car worth Rs. 1,50,000 was sold by X to Y at 5% profit. Y sold the car back to X at 20% loss. Therefore, who gained in the entire transaction?
(a) X gained Rs 31500
(b) X lost Rs 43500
(c) X gained Rs 3150
(d) X lost Rs 315000

Answer 1

Hint: It is given that X sold the car at 5% profit. Thus, the money paid by Y will be 5% more than the original cost of the car. Thus, we will find 5% of the original cost and add it to the original cost. This will be the first selling price. Now. Y sold it back to X at 20% loss. This means we have to find 20% of the first selling point and subtract it from the first selling point. Thus, we can find the money paid by X. Clearly X is in profit. So, to find the profit, we will subtract the money paid by X from the money gained by him in the first transaction. We can find x percent of the amount as $\dfrac{x}{100}\times a$.

Complete step-by-step answer:
Now, it is given that the worth of the car is 150000.
X sold the car to Y at 5% profit.
Thus, money paid by Y to X will be the sum of the worth of the car and 5% of the worth of the car.
5% of worth of car, i.e. 150000 will be $\dfrac{5}{100}\times 150000$ = Rs 7500
Thus, money paid by Y will be (150000 + 7500) = Rs 157500.
Now, Y sells the car back at loss of 20%. Thus, money paid by X to Y will be the difference of money paid by Y to X in the first transaction and 20% of the money paid by Y to X in the first transaction.
20% of the money paid by Y in the first transaction is given as $\dfrac{20}{100}\times 157500$ = Rs 31500
Thus, money paid by X to Y in the second transaction is (157500 – 31500) = Rs 126000.
Thus, money left with X is 157500 – 126000 = Rs 31500.
So, the correct answer is “Option A”.

Note: First 5% profit and then 20% profit is different from and yields different value than a collective 25% of profit. Here students need to keep in mind that the percentage profit/loss is calculated w.r.t to the cost price, that’s why we use Cost price in denominator while calculating percent profit and loss