Step 1: Understanding the Concept:
Money invested in a stock buys a certain number of shares at the price on that day, and the value of the holding the next day depends on the new price of the same number of shares.
Step 2: Key Formula or Approach:
Work out the gain or loss separately for each stock, using
\[ \text{Gain} = (\text{units held}) \times (\text{new price} - \text{old price}) \]
then add the two gains together to get the total profit.
Step 3: Detailed Explanation:
For Stock A, Rs. 100 at Rs. 50 per unit buys $\dfrac{100}{50}=2$ units. The price rises from Rs. 50 to Rs. 55, a gain of Rs. 5 per unit, so
\[ \text{Gain on A} = 2\times5=10 \text{ Rs.} \]
For Stock B, Rs. 80 at Rs. 80 per unit buys $\dfrac{80}{80}=1$ unit. The price falls from Rs. 80 to Rs. 70, a loss of Rs. 10 per unit, so
\[ \text{Loss on B} = 1\times(-10)=-10 \text{ Rs.} \]
Step 4: Combine the two results.
\[ \text{Total profit} = 10 + (-10) = 0 \]
Step 5: Final Answer:
The gain on Stock A exactly cancels the loss on Stock B, so the investor's overall profit is Rs. $0$, option (A).