GATE CSE 2021 Set 1 | GA Question: 7

Question

$$\begin{array}{|c|c|c|c|} \hline \textbf{Items} & \textbf{Cost} & \textbf{Profit %} & \textbf{Marked Price} \\ & \text{(₹)} & & \text{(₹)} \\\hline P &5,400 &---&5,860\\\hline Q&---&25&10,000\\\hline\end{array}$$

Details of prices of two items $P$ and $Q$ are presented in the above table. The ratio of cost of item $P$ to cost of item $Q$ is $3:4$. Discount is calculated as the difference between the marked price and the selling price. The profit percentage is calculated as the ratio of the difference between selling price and cost, to the cost 

$(\text{Profit} \%=\dfrac{\text{Selling price – Cost}}{\text{Cost}} \times 100)$

The discount on item $Q$, as a percentage of its marked price, is _______

• A.  $25$
• B. $12.5$
• C. $10$
• D. $5$

Answer 1

Option C

$\frac{\text{Cost of P}}{\text{Cost of Q}} = \frac{3}{4}\\\frac{5400}{\text{Cost of Q}} = \frac{3}{4}\\\text{Cost of Q} = 7200$

$\text{Profit %} = \frac{\text{Selling price – Cost}}{\text{Cost}} \times 100$

$\implies 25 = \frac{SP – 7200}{7200} \times 100 \implies SP = 9000$

$\text{Discount %} = \frac{10000 – 9000}{10000}\times100 = 10\%$