Find the cash realised by selling Rs. 2,440 nominal of 9.5% stock at a 4% discount, if brokerage is 1/4% on the market value.

Introduction / Context:
This question focuses on finding the net cash realised when selling a block of stock at a discount, after deducting brokerage. The holder has a certain nominal amount of 9.5% stock, but the dividend rate is not needed here because we are only concerned with sale proceeds, market value, and brokerage.

Given Data / Assumptions:

• Nominal (face) value of stock sold = Rs. 2,440.
• The stock is sold at a 4% discount, so market price per Rs. 100 nominal is Rs. 96.
• Brokerage rate on sale = 1/4% = 0.25% of the market value.
• We assume brokerage is deducted from the gross sale proceeds to find net cash realised.

Concept / Approach:
First find the gross sale value using the discounted market price. Then compute brokerage as a percentage of this gross value and subtract it to get net cash realised. The main formulas are:
gross sale value = nominal value * (market price per 100 / 100) brokerage = brokerage rate * gross sale value net cash realised = gross sale value - brokerage

Step-by-Step Solution:
Step 1: Market price per Rs. 100 nominal at 4% discount = 100 - 4 = Rs. 96. Step 2: Gross sale value for Rs. 2,440 nominal = 2440 * (96 / 100) = 2440 * 0.96 = Rs. 2,342.40. Step 3: Brokerage rate = 0.25% of gross sale value. Step 4: Brokerage amount = 0.25 / 100 * 2342.40 = 2342.40 * 0.0025 = Rs. 5.856. Step 5: Net cash realised = gross sale value - brokerage = 2342.40 - 5.856 = Rs. 2,336.544. Step 6: Rounding to two decimal places, net cash realised ≈ Rs. 2,336.54.

Verification / Alternative check:
We can check orders of magnitude: selling at Rs. 96 per Rs. 100 nominal means roughly 96% of Rs. 2,440, which is around Rs. 2,342. Deducting a very small brokerage of 0.25% of this amount must reduce the proceeds by less than Rs. 10. Subtracting a little under Rs. 6 gives about Rs. 2,336, so Rs. 2,336.54 is consistent with this approximation.

Why Other Options Are Wrong:
Values like Rs. 2,289.00 and Rs. 2,290.00 are too low and would correspond to a much larger effective discount or brokerage. Rs. 2,305.75 also implies higher charges than those given. Rs. 2,400.00 would be greater than the gross sale value at a discount, which is impossible. Only Rs. 2,336.54 is consistent with 4% discount and 0.25% brokerage.

Common Pitfalls:
Students may mistakenly compute brokerage on the face value instead of the market value, or they may add brokerage instead of subtracting it when dealing with a sale. It is crucial to distinguish purchase problems, where brokerage is added to cost, from sale problems, where brokerage reduces the cash received.

Final Answer:
The cash realised by selling the stock is approximately Rs. 2,336.54.