The cost price of a Rs. 100 face value stock quoted at a discount of Rs. 4, when brokerage is 1/4%, is equal to how many rupees per Rs. 100 nominal?

Introduction / Context:
This problem tests understanding of how to calculate the effective cost price of a stock when both a discount and brokerage are involved. Discount affects the quoted market price, while brokerage is an additional charge paid to the broker, usually calculated as a percentage of the nominal value or the market value depending on convention.

Given Data / Assumptions:

• Face (nominal) value of the stock = Rs. 100.
• The stock is quoted at a discount of Rs. 4, so quoted price = Rs. 96.
• Brokerage rate = 1/4% (that is, 0.25%).
• We assume brokerage is charged on the nominal value of Rs. 100, as is common in many exam problems.

Concept / Approach:
The total cost price for an investor buying Rs. 100 nominal of stock is the sum of the market price and brokerage. If P is the quoted market value and B is the brokerage per Rs. 100 nominal, then:
effective cost price = P + B We first find the quoted price after discount, then compute brokerage, and finally add the two to obtain the cost price per Rs. 100 nominal.

Step-by-Step Solution:
Step 1: Since the stock is at a discount of Rs. 4 on Rs. 100 nominal, quoted price P = 100 - 4 = Rs. 96. Step 2: Brokerage rate = 1/4% = 0.25% on Rs. 100 nominal. Step 3: Brokerage per Rs. 100 nominal B = (0.25 / 100) * 100 = Rs. 0.25. Step 4: Effective cost price per Rs. 100 nominal = P + B = 96 + 0.25 = Rs. 96.25. Step 5: Therefore, the investor effectively pays Rs. 96.25 for each Rs. 100 nominal of stock purchased.

Verification / Alternative check:
One can check by imagining purchase of several shares. For one Rs. 100 share, the investor pays Rs. 96 as price and Rs. 0.25 as brokerage, totalling Rs. 96.25. For any number of shares, the effective cost per Rs. 100 nominal remains Rs. 96.25, confirming the calculation.

Why Other Options Are Wrong:
Rs. 95.75 would imply subtracting brokerage instead of adding it, which is incorrect. Rs. 96 ignores brokerage entirely. Rs. 104.25 is higher than the nominal value and does not match any reasonable combination of discount and brokerage here. Rs. 100 corresponds to purchasing at par without discount or brokerage. Only Rs. 96.25 correctly incorporates both the Rs. 4 discount and the 1/4% brokerage on Rs. 100 nominal.

Common Pitfalls:
Students often calculate brokerage on the market price instead of the nominal value when the question implies otherwise, or they mistakenly subtract brokerage in a purchase scenario. It is important to read carefully whether brokerage is added to or subtracted from the price and whether it is calculated on face value or on market value.

Final Answer:
The correct cost price is Rs. 96.25 per Rs. 100 nominal of stock.