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:

Write the total portfolio value as (shares times price) added up for each stock, and read the phrase about B and C as 20 shares of B plus an unstated number of C shares. Instead of solving for the C shares alone, try setting the total number of shares as your one unknown from the start.

Answer 1

Correct Answer: 380

Approach: Portfolio value is just (shares \(\times\) price) summed across stocks. Fix what we know, leave C's count as the unknown, and solve one linear equation.

Step 1: Prices: \(A = 120\), \(B = 90\), \(C = 80\). Holdings: 60 of A, 20 of B, and \(n\) of C.

Step 2: Value of A and B: \[ 60 \times 120 = 7200, \qquad 20 \times 90 = 1800. \] Together that is \(9000\).

Step 3: Total value is 33000, so C must supply the rest: \[ 9000 + 80n = 33000 \;\Rightarrow\; 80n = 24000 \;\Rightarrow\; n = 300. \]

Step 4: Total shares held: \[ 60 + 20 + 300 = 380. \]

Final Answer: The trader holds \(\boxed{380}\) shares in all.

Answer 2

Approach: Compute the value already accounted for by A and B directly, and attribute the remainder entirely to C.

Value from \(60\) shares of A (at Rs. \(120\)): \(60\times120=7200\). Value from \(20\) shares of B (at Rs. \(90\)): \(20\times90=1800\). Together, A and B account for \[ 7200+1800=9000. \]
The remaining value must come from C (at Rs. \(80\) per share): \[ 33000-9000=24000 \implies \text{shares of C}=\frac{24000}{80}=300. \]
Total shares held \[ =60+20+300=\boxed{380} \]
(Reading "20 of B and C together" as 60 shares of A, 20 of B, and an unstated number of C: splitting only 20 shares between B and C could never reach the required Rs. 25,800 remaining value, so C must be counted separately.)

Answer 3

Concept:

• Total portfolio value equals the sum of (shares times price) for every stock held; since the number of A and B shares are already fixed, treat the total number of shares as the one unknown and write a single equation for it directly.
• Reading "20 of B and C together" as 20 shares of B plus an unstated number of C shares, the count of C shares can be written as (total shares minus the 80 shares already fixed for A and B), avoiding a separate final addition step.

Step 1: Let $T$ be the total number of shares held across all three stocks.
Shares of A $=60$, shares of B $=20$, so shares of C $= T - 80$.

Step 2: Write the total value equation directly in terms of $T$.
$120(60) + 90(20) + 80(T-80) = 33000$

Step 3: Expand and simplify.
$7200 + 1800 + 80T - 6400 = 33000$
$2600 + 80T = 33000$

Step 4: Solve for $T$.
$80T = 30400 \Rightarrow T = 380$

Final Answer: $380$ shares