A share of stock in the Lofty Cheese Company is quoted at [tex]$25 \frac{1}{4}$[/tex]. Suppose you hold 30 shares of that stock, which you bought at [tex]$20 \frac{1}{4}$[/tex]. If you sell your stock at [tex][tex]$25 \frac{1}{4}$[/tex][/tex], which one of the following statements would be true?

A) You'll make a profit of [tex]$\$15$[/tex].
B) You'll suffer a loss of [tex]$\[tex]$150$[/tex][/tex].
C) You'll suffer a loss of [tex]$\$15$[/tex].
D) You'll make a profit of [tex]$\[tex]$150$[/tex][/tex].



Answer :

Let's break down the problem step by step to determine the correct statement from the given options.

1. Sell Price of the Stock:

The quoted selling price of a share of stock in the Lofty Cheese Company is [tex]\( 25 \frac{1}{4} \)[/tex].
Converting this to a decimal, we get:
[tex]\[ 25 + \frac{1}{4} = 25 + 0.25 = 25.25 \text{ dollars} \][/tex]

2. Buy Price of the Stock:

The price you paid when buying the shares was [tex]\( 20 \frac{1}{4} \)[/tex].
Converting this to a decimal, we get:
[tex]\[ 20 + \frac{1}{4} = 20 + 0.25 = 20.25 \text{ dollars} \][/tex]

3. Number of Shares:

You hold [tex]\( 30 \)[/tex] shares of the stock.

4. Total Sell Amount:

To find the total sell amount, multiply the number of shares by the selling price per share:
[tex]\[ \text{Total Sell Amount} = 30 \times 25.25 = 757.5 \text{ dollars} \][/tex]

5. Total Buy Amount:

To find the total buy amount, multiply the number of shares by the buying price per share:
[tex]\[ \text{Total Buy Amount} = 30 \times 20.25 = 607.5 \text{ dollars} \][/tex]

6. Profit or Loss Calculation:

To determine whether you made a profit or suffered a loss, subtract the total buy amount from the total sell amount:
[tex]\[ \text{Profit or Loss} = 757.5 - 607.5 = 150 \text{ dollars} \][/tex]

Since the result is positive, it indicates a profit of \[tex]$150. So, the correct statement is: D) You'll make a profit of \$[/tex]150.