CAT 2025 Slot 1 QA Question 20

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CAT 2025 Slot 1QAAlgebra • Linear EquationEasy

Stocks A, B and C are priced at rupees 120, 90 and 150 per share, respectively. A trader holds a portfolio consisting of 10 shares of stock A, and 20 shares of stocks B and C put together. If the total value of her portfolio is rupees 3300, then the number of shares of stock B that she holds, is

TITA Answer:

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Official Convenor Answer Key: 15

Answer and solution

Answer: 15

📌 Core Concept

We are given a system of linear equations based on the total number of shares and their respective values. The governing formula is:

\text{Total Value} = (\text{Number of Shares} \times \text{Price per Share}) \text{ for each stock}

🔢 Step-by-Step Solution

Calculate the value of stock A:

Number of shares of A = 10

Price per share of A = 120

Value of A = 10 × 120 = 1200$ rupees

Set up equations for stocks B and C:

Let

x

be the number of shares of B.

Let

y

be the number of shares of C.

Total shares of B and C:

x + y = 20

Total value of B and C:

90x + 150y = 2100

(since total portfolio is 3300 and value of A is 1200)

Express

y

in terms of

x

y = 20 - x

Substitute

y

into the value equation:

90x + 150(20 - x) = 2100

Expand:

90x + 3000 - 150x = 2100

Combine like terms: - 60x + 3000 = 2100$

Solve for

x

: - 60x = -900 ⇒ x = 15$

⚡ 30-Second Shortcut

Since the total shares of B and C are 20, and the total value is 2100, the average price per share is 105.

Stock B is 90, which is 15 less than 105, and stock C is 150, which is 45 more than 105.

Let the number of B shares be

x

. The total deviation is - 15x + 45(20 - x) = 0$.

Simplify: - 15x + 900 - 45x = 0 ⇒ -60x = -900 ⇒ x = 15$.

🎯 Final Answer

Correct Answer: 15

CAT 2025 Slot 1 QA Question 20

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