Question

After deducting a commission of $10\% $ a TV costs $Rs.18000$. What is its gross value?
A) $18800$
B) $20000$
C) $19800$
D) None of these

Answer 1

Hint: We are given that after deducting a commission of $10\% $ a TV costs $Rs.18000$ and we need to find its gross value. Gross value is the total value of output produced. Let us suppose the gross value be $Rs.x$ and so reducing $10\%$ of $x$ will give us the cost of the TV. We will use this logic to find the gross value.

Complete step by step solution:
Let the gross value of TV be $Rs.x$
Commission on TV = $10\% $
Therefore, price of the TV after deducting the commission = $Rs.\left( {x - 10\% {\text{ }}of{\text{ }}x} \right)$
$ = \left( {x - \left( {\dfrac{{10}}{{100}} \times x} \right)} \right)$
On canceling-out common factors, we get
$ = \left( {x - \left( {\dfrac{x}{{10}}} \right)} \right)$
On opening bracket, we get
$ = \left( {x - \dfrac{x}{{10}}} \right)$
Take LCM
$ = \left( {\dfrac{{10x - x}}{{10}}} \right)$
On subtraction of like terms, we get
$ = \left( {\dfrac{{9x}}{{10}}} \right)$
The price of TV after deducting the commission = $Rs.18000$
$ \Rightarrow \left( {\dfrac{{9x}}{{10}}} \right) = 18000$
On cross-multiplication, we get
$ \Rightarrow 9x = 18000 \times 10$
On shifting $9$ to right-hand side, we get
$ \Rightarrow x = \dfrac{{18000 \times 10}}{9}$
On division, we get
$ \Rightarrow x = Rs.20,000$
Thus, after deducting a commission of $10\% $ a TV costs $Rs.18000$ and its gross value is $Rs.20,000$. So, the correct option is B.

Note:
Remember that gross refers to the total amount made as a result of some activity. It can refer to things such as total profit or total sales and net refers to the amount left over after all deductions are made. We need to know while taking the percentages on particular prices whether it has to be taken on the gross value or the cost price.