GATE CS 2021 Set 1 Q.7 (GA Q.7): Quantitative Aptitude

Prices and profit details of items P and Q
Items	Cost (₹)	Profit %	Marked Price (₹)
P	5,400	---	5,860
Q	---	25	10,000

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 $\left(\text{Profit}\% = \frac{\text{Selling price} - \text{Cost}}{\text{Cost}} \times 100\right)$ .

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

12.5

Official answer and solution

Official answer: C
From: Official GATE 2021 answer key

Solution

Determine the cost of Q from the given cost ratio, find the selling price from the profit percentage, and compute discount percentage relative to marked price.

Let $C_P$ and $C_Q$ denote the cost prices of items P and Q respectively. We are given $C_P = 5400$ and $\frac{C_P}{C_Q} = \frac{3}{4}$ .

Solving for $C_Q$ gives:

C_Q = 5400 \times \frac{4}{3} = 7200\text{ ₹}

The profit percentage on item Q is $25\%$ . Hence, the selling price of Q is:

\text{SP}_Q = C_Q \times \left(1 + \frac{25}{100}\right) = 7200 \times 1.25 = 9000\text{ ₹}

The marked price of item Q is $\text{MP}_Q = 10000\text{ ₹}$ . The discount on item Q is:

\text{Discount}_Q = \text{MP}_Q - \text{SP}_Q = 10000 - 9000 = 1000\text{ ₹}

The discount as a percentage of marked price is:

\frac{1000}{10000} \times 100 = 10\%

Final answer

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2021 Computer Science and Information Technology (CS, Set-1)
Question: 7 of 65, printed as GA Q.7
Section: General Aptitude

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