GATE CS 2021 Set 1 Q7 — General Aptitude

We can solve this step-by-step using the information provided in the table and the text:

1. Find the Cost Price of item $Q$ ($C_Q$):

   We are given that the Cost Price of item $P$ ($C_P$) is ₹$5,400$ and the ratio of the cost of $P$ to $Q$ is $3:4$.

   $$\frac{C_P}{C_Q} = \frac{3}{4}$$ $$C_Q = C_P \times \frac{4}{3} = 5400 \times \frac{4}{3} = 7200 \text{ ₹}$$
2. Find the Selling Price of item $Q$ ($S_Q$):

   The profit percentage on item $Q$ is $25\%$. Using the profit percentage formula:

   $$\text{Profit \%} = \frac{S_Q - C_Q}{C_Q} \times 100 = 25$$ $$S_Q = C_Q \times \left(1 + \frac{25}{100}\right) = 7200 \times 1.25 = 9000 \text{ ₹}$$
3. Calculate the Discount on item $Q$:

   The Marked Price of item $Q$ ($M_Q$) is ₹$10,000$.

   $$\text{Discount} = M_Q - S_Q = 10000 - 9000 = 1000 \text{ ₹}$$
4. Calculate the Discount Percentage of Marked Price: $$\text{Discount \%} = \frac{\text{Discount}}{M_Q} \times 100 = \frac{1000}{10000} \times 100 = 10\%$$

Therefore, the discount on item $Q$ as a percentage of its marked price is $10\%$.