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:
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:
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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.
Updated On: Jan 5, 2026
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Correct Answer: 15
Approach Solution - 1
The problem involves determining the number of shares of stock B in the trader's portfolio. Let the number of shares of stock B be x, and those of stock C be y. The given conditions are:
- The price of stock A is ₹120 per share, and the trader holds 10 shares of stock A.
- The combined number of shares of stocks B and C is 20. Thus, x + y = 20.
- The price of stock B is ₹90 per share, and the price of stock C is ₹150 per share.
- The total value of the portfolio is ₹3300.
First, calculate the value of stock A in the portfolio:
Total value of stock A = 10 × 120 = ₹1200
The remainder of the portfolio value comes from stocks B and C. Therefore,
Value of stocks B and C = 3300 - 1200 = ₹2100
The value of stocks B and C can also be expressed in terms of x and y:
90x + 150y = 2100
Now, solve the system of equations:
- From x + y = 20, express y as y = 20 - x.
- Substitute y = 20 - x into 90x + 150y = 2100:
90x + 150(20 - x) = 2100
90x + 3000 - 150x = 2100
-60x + 3000 = 2100
-60x = 2100 - 3000
-60x = -900
x = 15
Thus, the number of shares of stock B is 15. This value falls within the specified range [15, 15].
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Approach Solution -2
Step 1: Note the given values.
\[
P_A = 120,\quad P_B = 90,\quad P_C = 150.
\]
\[
N_A = 10,\quad N_B + N_C = 20.
\]
Total portfolio value:
\[
3300.
\]
Step 2: Use the share-count condition. \[ N_C = 20 - N_B. \]
Step 3: Write the total value equation. \[ 3300 = (10)(120) + (N_B)(90) + (20 - N_B)(150). \]
Step 4: Simplify. \[ 3300 = 1200 + 90N_B + 3000 - 150N_B. \] Combine constants and coefficients: \[ 3300 = 4200 - 60N_B. \] Rearrange: \[ 60N_B = 4200 - 3300 = 900. \] \[ N_B = \frac{900}{60} = 15. \] Thus, the trader holds: \[ \boxed{15} \] shares of stock B.
Step 2: Use the share-count condition. \[ N_C = 20 - N_B. \]
Step 3: Write the total value equation. \[ 3300 = (10)(120) + (N_B)(90) + (20 - N_B)(150). \]
Step 4: Simplify. \[ 3300 = 1200 + 90N_B + 3000 - 150N_B. \] Combine constants and coefficients: \[ 3300 = 4200 - 60N_B. \] Rearrange: \[ 60N_B = 4200 - 3300 = 900. \] \[ N_B = \frac{900}{60} = 15. \] Thus, the trader holds: \[ \boxed{15} \] shares of stock B.
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