Question

After selling a table worth Rs 12000 at a 20% loss, a trader buys a TV with the same money. Next, he sold the TV at a 20% profit. What is his profit/loss in the whole transaction?

Answer 1

Hint: Selling price (S.P.): This is the price at which an article is sold.
Cost price (C.P.): This is the price at which an article is purchased.
We can calculate loss occurred by the below-mentioned formula as cost price and loss percentage is given.
Percentage Loss: The loss percent can be calculated as;
\[Loss\% = 100\times \dfrac{\text{Loss}}{\text{Cost price}}\]
The selling price in the first case can be cost price for the second case.
We can calculate profit occurred by the below-mentioned formula as cost price and profit percentage is given.
Profit percentage formula: The profit percent can be calculated as:
\[Profit\% = 100\times \dfrac{\text{Profit}}{\text{Cost price}}\]

Complete step by step solution:
Cost Price of Table initially = $Rs.12000$
Loss on Sale of Table = $20\%$
\[Loss\% = 100\times \dfrac{\text{Loss}}{\text{Cost price}}\]
On substituting the corresponding values,
\[ 20\% = 100\times \dfrac{\text{Loss}}{12000}\]
On simplification,
$ \Rightarrow 20 = \dfrac{{Loss}}{{120}} $
$ \Rightarrow Loss = 120{\rm X}20 $
On further simplification,
\[ \Rightarrow Loss = 2400 \]
Loss on Sale of Table = Rs 2400
So money earned initially $= 12000 – 2400 = Rs. 9600$
Cost price of TV $= 9600$
Profit on sale of TV $= 20\%$
\[Profit\% = 100\times \dfrac{\text{Profit}}{\text{Cost price}}\]
On substituting the corresponding values,
\[ 20\% = 100\times \dfrac{\text{Profit}}{9600}\]
On simplification,
$\Rightarrow 20 = \dfrac{{Profit}}{{96}} $
$ \Rightarrow Profit = 96{\rm X}20 $
On further simplification,
\[ \Rightarrow Profit = 1920 \]
Profit on sale of TV= $Rs.1920$
$\text{Net loss= Loss – Profit}$
$=2400-1920$
$=Rs 480$

$\therefore$ The loss in the whole transaction=Rs.480

Note:
The gain or loss is always reckoned on the cost price.
In calculating profit percent and loss percent, sometimes after purchasing an article, we have to pay some more money for things like transportation, repairing charges, local taxes, these extra expenses are called overheads.
For calculating the total cost price, we add overheads to the purchase price or cost price.