Question

Angad sold the TV for rupees $Rs.15000$ making a profit of $25\% $. Find the CP of the TV.

Answer 1

Hint: First we will see what is cost price, selling price, profit, and loss.
Cost price is the original rate of the given product from the retailer, like a mobile phone cost price is fixed $Rs.10000$(making).
Selling price is the product sold price like if that mobile is sold at $Rs.12000$(for two thousand profit) or mobile is sold at $Rs.8000$ (two thousand rupees loss).
Profit is the gain that cost price is greater than selling price. Lose if the cost price is less than the selling price.
Formula used: $CP = \dfrac{{100}}{{(100 + P\% )}} \times SP$, where CP is the cost price and SP is the selling price and P is the profit. Similarly for the selling price formula is $SP = \dfrac{{(100 + P\% )}}{{100}} \times CP$

Complete step-by-step solution:
Given that Angad sold the TV for rupees $Rs.15000$ with the profit in the percentage as $25\% $.
And we need to find the cost price (as per the given)
Since selling price and profits are given in the information, we just need to substitute into the Cost price formula to find it.
Thus, we get, $CP = \dfrac{{100}}{{(100 + 25)}} \times 15000$ (SP is $Rs.15000$ and profit is $25\% $)
Further solving we get, $CP = \dfrac{{100}}{{125}} \times 15000$(in the denominator we use the operation called addition)
$CP = \dfrac{{100}}{{125}} \times 15000 \Rightarrow 100 \times 120$(By division operator we divide the selling price and denominator)
Finally, we get, $CP = 100 \times 120 \Rightarrow 12000$ (by multiplication operation)
Hence the cost price of the TV is $Rs.12000$. Also, the profit is $Rs.3000$.

Note: We can also able to check the given profit percentage is correct or wrong by using the cost and selling price as the cost price of the TV is $Rs.12000$ and selling price is $Rs.15000$
The profit formula is $P\% = \dfrac{{SP - CP}}{{CP}} \times 100$.
Apply the rupees of the cost and selling we get $P\% = \dfrac{{SP - CP}}{{CP}} \times 100 \Rightarrow \dfrac{{300000}}{{12000}} \Rightarrow 25\% $.