Question

Ram owns a plot worth $Rs.10,000$ . He sells it to Shyam at a profit of $10\% $ . After sometimes Shyam sells it back to Ram at a $10\% $ loss, then Ram overall.
(A) loses $Rs.100$
(B) loses $Rs.900$
(C) gains $Rs.100$
(D) gains $Rs.1100$

Answer 1

Hint:
Analyse the situation properly and notice that two transactions are going on in this problem. Start with finding the selling price of the plot when sold by Ram to Shyam. Then this selling price will be the cost price for the next transaction. Now find the price at which Ram bought the plot from Shyam. The difference in both the selling prices will be the overall gain or loss.

Complete Step by Step Solution:
Here in this question, Ram sold a plot to Shyam of worth $Rs.10,000$ at a profit of $10\% $ . Then after some time, Ram bought the same plot from Shyam at a loss of $10\% $. With this information, we need to find the overall loss or profit of Ram
Before starting with the solution, we must understand the concept of profit and loss. Profit is defined as the difference between the selling price and the cost price when the selling price is more than the cost price. Whereas, the loss is defined as the difference between the cost price and selling price when the cost price is more than the selling price.
$ \Rightarrow $ Profit $ = $ Selling Price $ - $ Cost Price and Profit$\% = \dfrac{{{\text{Selling Price}} - {\text{Cost Price}}}}{{{\text{Cost Price}}}} \times 100$
Also;
$ \Rightarrow $ Loss $ = $ Cost Price $ - $ Selling Price and Loss$\% = \dfrac{{{\text{Cost Price}} - {\text{Selling Price}}}}{{{\text{Cost Price}}}} \times 100$
In this case, Ram sold a plot of worth $Rs.10,000$ at a profit of $10\% $ . Therefore, the worth becomes the cost price of the plot, and the profit percentage will be $10\% $ .
According to the above formula for profit percentage, we have:
$ \Rightarrow $$10 = \dfrac{{{\text{Selling Price}} - 10000}}{{10000}} \times 100$
Now we can transform the above equation and find the unknown value of ‘Selling Price’
$ \Rightarrow 10 = \dfrac{{{\text{Selling Price}} - 10000}}{{10000}} \times 100 \Rightarrow 10 \times 100 = {\text{Selling Price}} - 10000$
Therefore, the selling price can be evaluated as:
$ \Rightarrow {\text{Selling Price}} = 10000 + 1000 = Rs.11000$
After this transaction, the plot is again sold to Ram by Shyam at a loss of $10\% $ and the selling price of the previous transaction will be the cost price for this one, i.e. by using the formula for the loss we get:
$ \Rightarrow $$10 = \dfrac{{11000 - {\text{Selling Price}}}}{{11000}} \times 100$
Now we can transform the above equation to find the unknown value of the new selling price
$ \Rightarrow 10 = \dfrac{{11000 - {\text{Selling Price}}}}{{11000}} \times 100 \Rightarrow 10 \times 110 = 11000 - {\text{Selling Price}}$
Therefore, the new selling price will be:
${\text{Selling Price}} = 11000 - 1100 = Rs.9900$
So, we can say that the Ram bought the plot again at a price $Rs.9900$
Thus, Ram sold the plot at $Rs.11000$ but bought it again at $Rs.9900$, i.e. he gains a profit of $11000 - 9900 = Rs.1100$

Hence, the option (D) is the correct answer

Note:
In questions like this, the use of the concepts of profit and loss always plays a crucial role. An alternate approach can be to use the concepts of the percentage to calculate the selling price using the formula, i.e. \[10\% = \left( {\dfrac{{{\text{Selling Price}}}}{{{\text{Cost Price}}}} - 1} \right) \times 100 \Rightarrow \dfrac{{{\text{Selling Price}}}}{{{\text{Cost Price}}}} = 1 + 0.1 = 1.1\] . Therefore, this can be used to find the selling price by multiplying the cost price with the ratio $1.1$.