Net cash realized on sale with brokerage: Find the cash realized by selling a 5.5% stock at 106 1/4 when brokerage is 1/4% of the sale proceeds (per ₹100 nominal).

Introduction / Context:
When selling stock, the quoted price is reduced by brokerage fees to obtain the net proceeds. Here we compute the net cash realized per ₹100 nominal given the sale price and brokerage rate.

Given Data / Assumptions:

• Selling price (quote) = 106 1/4 = 106.25 (per ₹100 nominal).
• Brokerage = 1/4% = 0.25% of the sale proceeds.
• We seek the net cash realized per ₹100 nominal.

Concept / Approach:
Net realized = Quote * (1 − brokerage%). Since brokerage is a percent of proceeds, directly multiply the sale price by (1 − 0.0025).

Step-by-Step Solution:
Gross sale = ₹106.25.Brokerage = 0.25% of 106.25 = 106.25 * 0.0025 = 0.265625.Net realized = 106.25 − 0.265625 = ₹105.984375 ≈ ₹106 (to nearest rupee).

Verification / Alternative check:
Using a factor: 106.25 * 0.9975 = 105.984375, same as the subtraction method. Rounding gives ₹106, matching the option list.

Why Other Options Are Wrong:

• “Rs. 1051/2” (105.5) and “1061/2” (106.5) are not the correct net after 0.25% brokerage.
• “None of these” is unnecessary since ₹106 is a reasonable rounded net.

Common Pitfalls:

• Applying brokerage to nominal value instead of sale proceeds, or forgetting to subtract it.

Final Answer:
Rs. 106