Q.A man holds ₹18,000 (nominal) of 12% stock and sells it at 90. He invests the entire sale proceeds in 15% stock available at 120. Find the change in his annual income.

Compute the old income, then the sale proceeds, then the nominal amount of the new stock those proceeds buy, then the new income, and finally the difference. …

Step 1 — Old annual income (interest on the ₹18,000 nominal held, at 12%):

Step 2 — Sale proceeds (selling ₹18,000 nominal at 90, i.e. ₹90 per ₹100 nominal):

Step 3 — Nominal value of the new stock (investing ₹16,200 in stock quoted at 120, i.e. ₹120 buys ₹100 nominal):

$\text{New nominal} = \dfrac{16200}{120}\times100 = ₹13{,}500$ …

Cross-check by yields. The old stock's yield $= \dfrac{12}{90}\times100 = 13.33\%$, on ₹16,200 of value $\Rightarrow 0.1333\times16200 ≈ ₹2{,}160$. The new stock's yield $= \dfrac{15}{120}\times100 = 12.5\%$, on the same ₹16,200 invested $\Rightarrow 0.125\times16200 = ₹2{,}025$. …

A frequent error is applying the new 15% rate to the old ₹18,000 nominal, ignoring that selling at 90 and rebuying at 120 changes how much nominal stock the proceeds can buy. Always recompute the new nomin …