Question

A house worth Rs. 1,50,000 is sold by X to Y at $5\% $ profit Y sells the house back to X at $2\% $ loss. Then the entire transaction:
A.X losses Rs. 1350
B.X gains Rs. 3150
C.X losses Rs. 4350
D.X gains Rs. 4350

Answer 1

Hint: To find the selling price of the house for X, apply the formula of S.P i.e.
$ \Rightarrow S.P = \dfrac{{100 + P\% }}{{100}} \times C.P$
Where S.P is the selling price, C.P is the cost price and P is the profit percent.
The selling price of the house for X will become Cost price of the house for Y. As Y sells the house back to X. So, we can calculate the Selling price of the house for Y by applying above formula but in place of profit, take loss i.e. L and change the sign to negative.
Now, you can calculate the final amount left with X after purchasing the house by taking the difference of selling price of X and selling price of Y.

Complete step-by-step answer:
We are given the cost price of the house for X. X sells the house to Y at $5\% $ profit. So, we can calculate the S.P of the house for X i.e.
$ \Rightarrow S.{P_X} = \dfrac{{100 + P\% }}{{100}} \times C.{P_X}$ …..(1)
Where $C.{P_X}$ is the cost price of the house for X, P% is the loss percent and $S.{P_X}$ is the selling price of the house for X.
We have given the Cost price of the house for X and profit percent i.e.
$ \Rightarrow C.{P_X} = Rs.1,50,000$
$ \Rightarrow P\% = 5\% $
Put these values in equation 1 we get,
$ \Rightarrow S.{P_X} = \dfrac{{100 + 5}}{{100}} \times 1,50,000$
By adding the numbers in numerator and cancelling 100 with 1,50,000 we get,
$ \Rightarrow S.{P_X} = 105 \times 1,500$
By multiplying these two numbers we get,
$ \Rightarrow S.{P_X} = 1,57,500$ …….(2)
Selling price of the house for X will become the cost price of the house for Y as Y purchases the house from X. Then the C.P of the house for Y is 1,57,500.
Then Y sells the house back to X at $2\% $ loss. Now, you can calculate the selling price of Y by the formula given below:
$ \Rightarrow S.{P_Y} = \dfrac{{100 - L\% }}{{100}} \times C.{P_Y}$ …….(3)
Where $C.{P_Y}$is the cost price of the house for Y, L% is the loss percent and $S.{P_Y}$is the selling price of the house for Y.
Put the value of all the parameters in equation 3 we get,
$ \Rightarrow S.{P_Y} = \dfrac{{100 - 2}}{{100}} \times 1,57,500$
Now, by subtracting the numbers in numerator and cancelling 100 with 1,57,500 we get,
$ \Rightarrow S.{P_Y} = 98 \times 1,575$
By multiplying these two numbers we get,
$ \Rightarrow S.{P_Y} = 1,54,350$ ……..(4)
As Y sells the house back to X then X gains or losses, it can be calculated by taking difference of selling price of the house for X and selling price of the house for Y and can be denoted by G/L i.e.
$ \Rightarrow G/L = S.{P_X} - S.{P_y}$ ……(5)
Put the value of equation 2 and 4 in equation 5 we get,
$ \Rightarrow G/L = 1,57,500 - 1,54,350$
By subtracting these two numbers we get,
$ \Rightarrow G/L = 3,150$
As the answer comes in positive. Therefore, X gains Rs. 3,150 in the whole transaction.
Hence, option B is the correct answer.

Note: Students can make mistakes in finding the selling price of a house for Y, they take Rs.1,50,000 instead of Rs. 1,57,500. As they take the cost price but it is wrong, the cost price of house for Y is the selling price of house for X. X sells the house so it becomes its selling price but Y purchases it, so it becomes its cost price.
Second mistake done by them is to add the loss in the formula. Loss always subtract from cost price as a person loses some money. So, take care of this profit always add into C.P while loss subtract from C.P to obtain S.P.