Question

A man sells two houses at the rate of $₹1.95$ lac each on one. He gains $5\%$ and on other he lost $5\%$ find his gain or loss percent in the whole transaction.

Answer 1

Step $\mathbf{1}$ : Find the cost price of first house.

Selling price of first house $=₹195000$

Gain percentage on first sale $=5\%$

Cost price of first house $=\frac{SP\times 100}{100+Gain\%}$

$$\begin{gathered} =₹\frac{195000\times 100}{100+5} \\ =₹\frac{19500000}{105} \\ =₹185714.285 \end{gathered}$$

Step $\mathbf{2}$ : Find the cost price of second house.

Now, Selling price of second house $=₹195000$

Loss percentage on second sale $=5\%$

Cost price of second house $=\frac{SP\times 100}{100-Loss\%}$

$$\begin{gathered} =₹\frac{195000\times 100}{100-5} \\ =₹\frac{19500000}{95} \\ =₹205263.157 \end{gathered}$$

Final Step : Find the overall loss or gain percentage.

Total selling price of the house $=₹(195000+195000)=₹390000$

Total cost price of the house $=₹(185714.285+205263.157)=₹390977.442$

Since, the cost price is greater than the selling price, loss has been occurred in the transaction.

So, Loss $=C.P.-S.P.=₹(390977.442-390000)=₹977.442$

Hence, loss percentage $=\frac{loss}{c.p.}\times 100$

$$\begin{gathered} =\frac{977.442}{390977.442}\times 100 \\ =0.25\% \end{gathered}$$

Hence, the man will sell the two houses at a loss of $\mathbf{0}\mathbf{.}\mathbf{25}\mathbf{\%}$.