A house was sold for Rs.12, 600 at a profit of 5% on the cost price. What percent would have been gained if it had been sold for Rs.13, 000?

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Hint: Here we will find the cost price of the house using the given selling price and profit percentage. As we are given the selling price and profit percentage we are forced to find the cost price of the house. With the help of the found cost price, we will find the percentage of profit when the house is sold for the new price because we are told to find the percentage of gain.

Formula Used:
We use formula of \[CP = \dfrac{{100 \times SP}}{{100 + profit \, percentage}}\]
Cost price (C.P.): This is the price at which an article is purchased.
Selling price (S.P.): This is the price at which an article is sold.

Complete step by step answer:
Here it is given that the selling price of the house is Rs.12600. Which is sold with a profit of 5%.
That is SP of the house = Rs.12, 600 and Profit=5%
We should find the cost price of the house using the given with the help of the formula given below
\[CP = \dfrac{{100 \times SP}}{{100 + profit \, percentage}}\]
On substituting the values we know in the above formula we get,
\[CP = \dfrac{{100 \times 12600}}{{100 + 5}}\]
On solving the above-given equation we find the cost price.
\[CP = 12000\]
Hence, the Cost Price of the house is Rs.12000
We have to find the percentage of profit if the house is sold for Rs.13000
We know that \[Gain \% = \dfrac{{SP - CP}}{{CP}} \times 100\% \]
Here Selling price is 13000 and the cost price is 12000.
 \[Gain\% = \dfrac{{13000 - 12000}}{{12000}} \times 100\% \]
On solving this we get,
\[Gain\% = \dfrac{{100}}{{12}}\% = 8\dfrac{1}{3}\% \]
If the house is sold for Rs.13000 the percentage of gain is \[8\dfrac{1}{3}\% \]

$\therefore$ The required % gain is \[8\dfrac{1}{3}\% \].

Note:
Profit or Gain: If the selling price is more than the cost price, the difference between them is the profit incurred.
Profit or Gain = S.P. – C.P
The amount of money that is spent to produce goods or services before any profit is added for the manufacturer or producer, or the price that a store, etc. pays for goods that it is going to sell.
Here initially we are provided a percentage of profit to which a house is sold, and we are told to find the percentage of profit if it is sold for some price which is higher than the initial amount. So we are tricked initially to find the cost price of the house.