Rajan invests Rs. 1,00,000 in foreign stocks when the exchange rate is 75 rupees per unit of foreign currency. After one year, his investment grows by 20 percent in foreign currency terms. He then converts the full amount back to Indian rupees at an exchange rate of 80. What is his real return in percentage terms measured in rupees?

Introduction / Context:
This question combines percentage returns on an investment with currency exchange rate fluctuations. It tests understanding of how investment growth in foreign currency and changes in the exchange rate together affect the final return when measured in domestic currency, here Indian rupees.

Given Data / Assumptions:

• Initial investment in rupees = Rs. 1,00,000.
• Initial exchange rate = 75 rupees per unit of foreign currency.
• Investment grows by 20 percent in foreign currency terms after one year.
• Final exchange rate when converting back to rupees = 80 rupees per unit of foreign currency.
• We must find the overall gain or loss percentage in rupee terms.

Concept / Approach:
First convert the rupee investment into foreign currency units using the initial exchange rate. Then apply the 20 percent growth to find the final amount in foreign currency. Finally, convert that amount back to rupees using the new exchange rate. The change from the original rupee investment to the final rupee amount provides the net gain or loss percentage. This is essentially a product of an investment growth factor and a currency movement factor.

Step-by-Step Solution:
Initial rupee investment = 1,00,000. Initial exchange rate = 75 rupees per foreign unit. Foreign currency units purchased = 1,00,000 / 75. Compute this: 1,00,000 / 75 = 1333.333... units approximately. After 20 percent growth in foreign currency terms, foreign amount = 1333.333... * 1.20 = 1600 units. Final exchange rate = 80 rupees per foreign unit. Final rupee amount = 1600 * 80 = 1,28,000 rupees. Net gain in rupees = 1,28,000 - 1,00,000 = 28,000 rupees. Gain percentage = 28,000 / 1,00,000 * 100 = 28 percent.

Verification / Alternative check:
We can also see this as a combined multiplicative effect. The foreign investment grows by a factor of 1.20, while each foreign unit is now worth 80 / 75 times as many rupees due to the exchange rate change. Overall factor on rupees = 1.20 * (80 / 75) = 1.20 * 1.0666... ≈ 1.28. This is exactly a 28 percent gain, confirming the previous calculation.

Why Other Options Are Wrong:
Loss of 24% or loss of 28%: These would only occur if the currency movement or investment return were negative overall, which is not the case here. Gain of 20%: This ignores the additional positive effect of the currency appreciation from 75 to 80. Only a gain of 28 percent correctly combines both sources of increase.

Common Pitfalls:
Candidates may forget to account for the change in exchange rate and only calculate the 20 percent investment growth. Others may incorrectly treat the exchange rate change as a simple addition in percentages. Always convert to foreign currency, apply the investment growth, then convert back with the new rate to see the true effect in domestic currency.

Final Answer:
Rajan earns a real return of 28% in rupee terms.