Question

Stocks A, B and C, at 120, 90 and 80 rs respectively. A trader holds a portfolio consisting 60 shares of A, 20 of B and C together. If total value is 33000 what is the number of shares he holds.

Hint:

When faced with a word problem where the given numbers lead to a logical contradiction, state the contradiction clearly and make a reasonable assumption about a likely typo to proceed with the solution.

Answer 1

Correct Answer: 380

Step 1: Understanding the Question:
The problem asks for the total number of shares a trader holds. We are given the prices of three stocks (A, B, C), the number of shares for A and B, and the total value of the portfolio. The number of shares of C is unknown.
Step 2: Key Formula or Approach:
The total value of a stock portfolio is the sum of the values of each individual stock holding. The value of a single stock holding is the number of shares multiplied by the price per share.
\[ \text{Total Value} = (n_A \times P_A) + (n_B \times P_B) + (n_C \times P_C) \] We will use this formula to solve for the unknown number of shares of C.
Step 3: Detailed Explanation:
Let's list the given information:
- Price of Stock A, \(P_A = 120\) rs
- Price of Stock B, \(P_B = 90\) rs
- Price of Stock C, \(P_C = 80\) rs
- Number of shares of A, \(n_A = 60\)
- Number of shares of B, \(n_B = 20\)
- Number of shares of C, \(n_C\) is unknown.
- Total portfolio value is assumed to be 33000 rs due to the inconsistency noted in Step 1.
Using the portfolio value formula:
\[ (n_A \times P_A) + (n_B \times P_B) + (n_C \times P_C) = 33000 \] Substitute the known values into the equation:
\[ (60 \times 120) + (20 \times 90) + (n_C \times 80) = 33000 \] \[ 7200 + 1800 + 80n_C = 33000 \] \[ 9000 + 80n_C = 33000 \] Now, solve for \(n_C\):
\[ 80n_C = 33000 - 9000 \] \[ 80n_C = 24000 \] \[ n_C = \frac{24000}{80} = 300 \] So, the trader holds 300 shares of stock C.
The question asks for the total number of shares he holds.
Total Shares = \(n_A + n_B + n_C\)
Total Shares = \(60 + 20 + 300 = 380\)
Step 4: Final Answer:
Based on the logical correction of the total value, the total number of shares the trader holds is 380.