ardz24 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
I'm confused how to set up the formulas here. Can any experts help?
If he made a 20% profit, then we know that the selling price, 96, was 20% greater than the cost, which we can call C. Algebraically: 96 = C + .2C --> 96 = 1.2C ---> 96/1.2 = C --> 960/12 = C --> 80 = C
So, for half the shares, he earned a profit of 96 - 80 = 16.
If he incurred a 20% loss, we know that the selling price, 96 was 20% less than the cost, which we can call X. Algebraically: 96 = C - .2C --> 96 = .8C ---> 96/.8 = C --> 960/8 = C --> 120 = C
So half the shares he suffered a loss of 96-120 = -24.
The average of the profit and loss = [16 + (-24)]/2 ---> -8/2 = -4. At 100 shares: -4 * 100 = -400. The answer is
C.
(Note you could also say that his total profit is 16*50 = 800. His total loss is 24*50 = 1200. His net is 800-1200 = -400.)
