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
OA C
Source: Veritas Prep
John sold 100 shares of stock for $96 per share. For half
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Let x be the ORIGINAL price of each share that sold for a 20% PROFITBTGmoderatorDC 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
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
Total selling price $9,600
For 50 shares it is 20% profit and for other 50 it is 20% Loss.
For 20% profit, we have
6/5*cost=9,600
cost = $80.
Now, for 20% loss, we have
4/5*cost=9,600
cost = $120.
Thus, total cost = 80*50 + 120*50 = 10,000
Hence, Loss = 10,000 - 9,600 = $400.
Option C is the correct answer. Regards!
For 50 shares it is 20% profit and for other 50 it is 20% Loss.
For 20% profit, we have
6/5*cost=9,600
cost = $80.
Now, for 20% loss, we have
4/5*cost=9,600
cost = $120.
Thus, total cost = 80*50 + 120*50 = 10,000
Hence, Loss = 10,000 - 9,600 = $400.
Option C is the correct answer. Regards!
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Let's let c = cost and r = revenue. For the shares experiencing a 20% profit we have: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
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
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