Annual income from investment at a premium: What annual income will be derived by investing ₹1547 in 13% Railway stock quoted at 119?

Introduction / Context:
When buying at a premium (e.g., 119), your cash investment exceeds the nominal obtained. Income still equals coupon rate times nominal value. So first find nominal purchased, then apply the 13% coupon.

Given Data / Assumptions:

• Investment (cash) = ₹1547.
• Quote = 119 ⇒ price factor = 1.19 per ₹1 nominal.
• Coupon rate = 13% per annum.

Concept / Approach:
Nominal purchased N = 1547 / 1.19. Then income = 0.13 * N. Compute N exactly if possible.

Step-by-Step Solution:
N = 1547 / 1.19 = 1300 (since 1.19 * 1300 = 1547).Annual income = 13% of 1300 = 0.13 * 1300 = ₹169.

Verification / Alternative check:
Direct check of multiplication 1.19 * 1300 = 1547 confirms the exact nominal, and 13% of 1300 is unambiguously ₹169.

Why Other Options Are Wrong:

• ₹189, ₹179, ₹159 do not match 13% of the precise nominal purchased.

Common Pitfalls:

• Applying 13% to the cash investment instead of the nominal value.

Final Answer:
Rs. 169