Question

Under pro-rata allotment, a company receives applications for 20,000 shares but allots only 10,000 shares to applicants. If a shareholder was allotted 400 shares under this scheme, how many shares did they originally apply for?

• A. \( 800 \text{ shares} \)
• B. \( 200 \text{ shares} \)
• C. \( 400 \text{ shares} \)
• D. \( 600 \text{ shares} \)

Hint:

When an issue is oversubscribed, an individual's applied shares will always be greater than their allotted shares. If your calculation results in a smaller number, you accidentally reversed your adjustment fraction.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
"Pro-rata allotment" is a method of dealing with oversubscription where every applicant receives some shares, but in a reduced proportion.
To find out individual details, we must first establish the "Allotment Ratio" of the whole group.
This ratio tells us how many shares were given for every share applied for.
Key Formula or Approach:
\[ \text{Shares Applied} = \text{Shares Allotted} \times \left( \frac{\text{Total Applications Received}}{\text{Total Shares Allotted}} \right) \]
Step 2: Detailed Explanation:
1. Calculate the General Ratio:
Total Applications = 20,000
Total Allotted = 10,000
Ratio = $\frac{20,000}{10,000} = 2 : 1$
This means for every 1 share allotted, the applicants must have applied for 2 shares.
2. Apply the ratio to the specific shareholder:
The shareholder was allotted 400 shares.
Using the ratio ($2/1$):
\[ \text{Shares Applied} = 400 \times \frac{2}{1} = 800 \text{ shares} \]
Step 3: Final Answer:
The shareholder originally applied for 800 shares.
Note: If the question asked how many shares they were allotted based on applying for 800, we would use the reciprocal ($1/2$).