Question

By selling two houses for Rs. 246400 each a man gained \[12\% \] on one house and lost \[12\% \] on the other. Find his total gain or loss.

Answer 1

Hint: First, we will find the value of the cost price of the first house by using formula. Then, we will get the profit amount by subtracting C.P. from S.P. Then, we will find the cost price of the second house using the formula. Then we will get the value of the loss received from the second house. Then we will get the total loss amount by subtracting the profit of the first house from the loss of the second one.

Complete step-by-step answer:
The selling price of the two houses is Rs. 246400.
Let the cost price of the first house be Rs. x
The profit gained from selling first house is \[12\% \].
The cost price can be determined by using the given formula
  \[ \Rightarrow C.P. = \dfrac{{100}}{{100 + profit\% }} \times S.P.\]
Now putting the value of C.P., profit and S.P. in the above equation, we get
 \[ \Rightarrow x = \dfrac{{100}}{{100 + 12}} \times 246400\]
On simplification, we get
 \[ \Rightarrow x = \dfrac{{100}}{{112}} \times 246400\]
Simplifying and we get the value of x
 \[ \Rightarrow x = 220000\]
Therefore, the cost price of the house is Rs. 220000.
Therefore, profit gained after selling the first house is calculated by the difference of selling price and cost price.
 \[ \Rightarrow profit = S.P. - C.P\]
Putting the value of S.P. and C.P. here, we get
 \[ \Rightarrow profit = 246400 - 220000\]
Hence on simplification we have,
 \[ \Rightarrow profit = 26400\]
Therefore, the profit gained by selling the first house is Rs. 26400.

The selling price of the two houses is Rs. 246400.
Let the cost price of the second house be Rs. y
The loss from selling second house is \[12\% \].
The cost price can be determined by using the given formula
 \[ \Rightarrow C.P. = \dfrac{{100}}{{100 - loss\% }} \times S.P.\]
Putting the value of C.P., S.P. and loss here, we get
 \[ \Rightarrow y = \dfrac{{100}}{{100 - 12}} \times 246400\]
On simplification, we get
 \[ \Rightarrow y = \dfrac{{100}}{{88}} \times 246400\]
Simplifying and we get the value of y.
 \[ \Rightarrow y = 280000\]
Therefore, the cost price of the second house is Rs. 280000.
Since, the cost price is higher than the selling price. Therefore, it is a loss.
Loss can be determined by the difference of C.P. and S.P.
 \[ \Rightarrow Loss = C.P. - S.P\]
Putting the value of C.P. and S.P., we get
 \[ \Rightarrow Loss = 280000 - 246400\]
Hence on simplification we get,
 \[ \Rightarrow Loss = 33600\]
Since the loss received from the second house is greater than the profit gained from the first house. Therefore, it is an overall loss.
The overall loss after selling both the houses is calculated by subtracting the profit of the first house from the loss of the second house.
 \[ \Rightarrow Overall\,\,Loss = 33600 - 26400\]
On simplification we get,
 \[ \Rightarrow Overall\,\,Loss = 7200\]
Therefore, the overall loss is Rs. 7200.

Note: If the cost price is greater than the selling price, then it is a loss.
And, if the selling price is greater than cost price, then it is a profit.
If the loss is greater than profit, then the net result will be loss.