Problem Solving

BTGmoderatorDC wrote:John sold 100 shares of stock for $96 per share. For half his shares, this represented a 20% profit; for the other half, this represented a 20% loss. What was the net gain or net loss on this sale of stock?

A. No loss or gain
B. Gain of $400
C. Loss of $400
D. Gain of $800
E. Loss of $800

Let x be the ORIGINAL price of each share that sold for a 20% PROFIT
So, 1.2x = price of each share that sold for a 20% profit
In other words, 1.2x = $96
So, x = 96/1.2 = $80
So, these shares ORIGINALLY cost $80 each

Let y be the ORIGINAL price of each share that sold for a 20% LOSS
So, 0.8x = price of each share that sold for a 20% loss
In other words, 0.8x = $96
So, x = 96/0.8 = $120
So, these shares ORIGINALLY cost $120 each

Let's first determine how much money John spent to BUY the 100 shares
50 shares at $80 apiece cost $4000
50 shares at $120 apiece cost $6000
TOTAL cost to BUY = $4000 + $6000 = $10,000

Now determine how much money John RECEIVED when we SOLD the 100 shares
Since he sold all 100 shares for $96 each, the TOTAL amount received = $9600

So, John SPENT $10,000 and he RECEIVED $9600
This represents a LOSS of $400

Answer: C

Cheers,
Brent

BTGmoderatorDC wrote:John sold 100 shares of stock for $96 per share. For half his shares, this represented a 20% profit; for the other half, this represented a 20% loss. What was the net gain or net loss on this sale of stock?

A. No loss or gain
B. Gain of $400
C. Loss of $400
D. Gain of $800
E. Loss of $800

Let's let c = cost and r = revenue. For the shares experiencing a 20% profit we have:

Profit = 0.2c

r - c = 0.2c

r = 1.2c

Since r = 96, we have:

96 = 1.2c

80 = c

So the profit was 96 - 80 = 16 dollars per share for 50 shares of stock.

For the shares experiencing a 20% loss, we have:

Profit = -0.2c

r - c = -0.2c

r = 0.8c

Since r = 96, we have:

96 = 0.8c

120 = c

So the loss was 120 - 96 = 24 dollars per share for the other 50 shares of stock.

Thus, the total net loss is 24(50) - 16(50) = (24 - 16)(50) = 8(50) = 400 dollars.

Answer: C