How many shares of face value Rs 25 each can be purchased for a total investment of Rs 12,750 if brokerage is charged at 2% on the purchase price?

Introduction / Context:
Questions about shares and brokerage are common in quantitative aptitude and finance-related competitive exams. They test your ability to correctly interpret what part of the investor's money goes into buying the shares, and what part goes toward brokerage or commission. In this problem, you are given the face value per share, the total amount available to invest (including brokerage), and the brokerage rate. You must calculate how many shares can be bought, taking brokerage into account.

Given Data / Assumptions:

• Face (market) value of each share = Rs 25.
• Total amount paid by the investor = Rs 12,750, and this includes the brokerage cost.
• Brokerage rate = 2% of the actual cost of shares purchased.
• The brokerage is assumed to be charged on the amount spent on the shares (standard convention).
• You must find the number of shares that can be purchased with Rs 12,750 under these conditions.

Concept / Approach:
Let the total amount actually spent to buy the shares (excluding brokerage) be X rupees. Brokerage is charged at 2% of this purchase amount, that is 0.02 * X. The total money paid by the investor equals the cost of the shares plus brokerage: X + 0.02 * X = 1.02 * X. You know that this total is Rs 12,750, so you can solve for X. Once you know X, you can divide it by the price per share (Rs 25) to get the number of shares. This linear equation approach is standard for problems involving commission or brokerage.

Step-by-Step Solution:
1. Let X be the total rupees spent on buying shares only (excluding brokerage). 2. Brokerage charged at 2% of X is 0.02 * X rupees. 3. The investor's total payment, including brokerage, is X + 0.02 * X = 1.02 * X. 4. You are told that 1.02 * X = 12,750 rupees, so solve for X: X = 12,750 / 1.02 = 12,500 rupees. 5. Each share costs Rs 25, so the number of shares = X / 25 = 12,500 / 25 = 500 shares.

Verification / Alternative check:
To verify the answer, calculate the brokerage and total amount with 500 shares. The cost of 500 shares at Rs 25 each is 500 * 25 = Rs 12,500. Brokerage at 2% is 2/100 * 12,500 = Rs 250. The total amount that would be paid is 12,500 + 250 = Rs 12,750, which matches the amount given in the question. This confirms that 500 shares is the correct number.

Why Other Options Are Wrong:
Option A, 450 shares, would cost 450 * 25 = Rs 11,250 and, with 2% brokerage, only total Rs 11,250 + 225 = Rs 11,475, which is less than Rs 12,750. Option B, 475 shares, would cost 11,875 with brokerage 237.5, totaling Rs 12,112.5, again not matching Rs 12,750. Option D, 525 shares, would cost 13,125 with brokerage 262.5, totaling Rs 13,387.5, which exceeds the available Rs 12,750. Only 500 shares exactly fit the given total amount when brokerage is included.

Common Pitfalls:
A common error is to subtract brokerage directly from the total amount without setting up the proper equation; for example, computing brokerage as 2% of Rs 12,750 instead of 2% of the purchase amount X. This leads to incorrect values. Another pitfall is misinterpreting whether brokerage is included in or added to the quoted price per share. Carefully reading the wording "for Rs 12,750, brokerage being 2%" indicates that the brokerage is part of the total payment, not in addition to a separate budget. Always set up a clean equation reflecting that total paid = cost of shares + brokerage.

Final Answer:
The investor can purchase 500 shares of face value Rs 25 each when brokerage is 2% and the total amount paid is Rs 12,750.