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:

Hint:

When the total number of shares of two assets is fixed, express one in terms of the other and substitute into the value equation. This reduces the problem to a simple linear equation.

Answer 1

Correct Answer: 15

Step 1: Let \(b\) and \(c\) be the number of B and C shares, with \(b+c=20\). The total portfolio value equation is \(10(120)+90b+150c=3300\), i.e. \(90b+150c=2100\).
Step 2: Substitute \(c=20-b\): \(90b+150(20-b)=2100 \Rightarrow 90b+3000-150b=2100 \Rightarrow -60b=-900\).
Step 3: Solve: \(b = \dfrac{900}{60} = 15\).
\[ \boxed{b = 15} \]