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CAT 2025Slot 1QAQuestion & Solution

AlgebraMedium

Question

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

Solution

1. Concept Used

  • Topic: Linear Equations / Ratio and Proportion
  • Formula: $$\text{Total Portfolio Value} = (\text{Shares of A} \times P_A) + (\text{Shares of B} \times P_B) + (\text{Shares of C} \times P_C)$$

2. Calculation

Let the number of shares of stock B held by the trader be $$x$$. Since the total shares of B and C together is 20, the number of shares of stock C is $$(20 - x)$$.

The prices are: Stock A = ₹120, Stock B = ₹90, Stock C = ₹150. The trader holds 10 shares of A.

Setting up the equation for total portfolio value:

$$10 \times 120 + 90 \times x + 150 \times (20 - x) = 3300$$

$$1200 + 90x + 3000 - 150x = 3300$$

$$4200 - 60x = 3300$$

$$60x = 4200 - 3300$$

$$60x = 900$$

$$x = \frac{900}{60} = 15$$

This makes intuitive sense: holding more of the cheaper stock B (₹90) and fewer of the expensive stock C (₹150) brings the portfolio value down from its maximum, which perfectly balances to ₹3300.

3. Solution

Answer = 15 ✅

The final calculated value is 15 shares of stock B.