Question

By investing ₹4650 in a \(7 \frac{1}{2} \%\)% stock, a person obtains an income of ₹300. The market price of the stock is:

• A. ₹116.25
• B. ₹114.50
• C. ₹120.75
• D. ₹118.35

Answer 1

The Correct Option is A

To determine the market price of the stock, we start by understanding the relation between the investment, the income obtained, and the stock's rate of interest.

Given:

• Investment: ₹4650
• Income: ₹300
• Rate of Stock: \(7 \frac{1}{2} \% = \frac{15}{2} \%\)

To find the market price, use the formula for the market value of the stock based on the yield:

\[ \text{Income} = \left(\frac{\text{Investment} \times \text{Rate of Stock}}{\text{Market Price per Unit}}\right) \]

Rearrange this to find the market price:

\[ \text{Market Price per Unit} = \left(\frac{\text{Investment} \times \text{Rate of Stock}}{\text{Income}}\right) \]

Substitute the given values:

\[ \text{Market Price per Unit} = \left(\frac{4650 \times \frac{15}{2}}{300}\right) \]

Calculate the above expression:

\[ = \left(\frac{4650 \times 7.5}{300}\right) \]

\[ = \left(\frac{34875}{300}\right) \]

Upon calculating,

\[ = 116.25 \]

Therefore, the market price of the stock is ₹116.25.