Profit/Loss Question

MattKoch wrote:Again, another easy problem that i cant seem to find the conclusion too. Sorry for the inconvenience of threads.

Bobby bought two shares of stock, which he sold for 96$ each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares combined Bobby had,

A. a profit of $10
B. a profit of $8
C. a loss of $8
D. a loss of $10
E. neither a profit nor a loss

My original answer was E. I cant seem to find why its wrong. Thanks.

Cost of the share on which Bobby had 20% profit = 96/1.2 = 80 $
Cost of the share on which Bobby had 20% loss = 96/0.8 = 120 $

So, Total cost incurred = 120+80 = 200$
Sale price = 96 + 96 = 192 $
Hence loss = 200 - 192 = 8$, C

Say he bought X type of stock in a$ each & Y of stock in b$ eack. Final sell price 96$/share for both X & Y type stock.

X : a’s 120% is 96 and Y : b’s 80% is 96

a * 120 / 100 = 96 ; a = 80$  Profit 16$ each share
b * 80/100 = 96 ; b = 120$  Loss 24$ each share

Finally loss of 8$ Hence : IMO C

MattKoch wrote:Again, another easy problem that i cant seem to find the conclusion too. Sorry for the inconvenience of threads.

Bobby bought two shares of stock, which he sold for 96$ each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares combined Bobby had,

A. a profit of $10
B. a profit of $8
C. a loss of $8
D. a loss of $10
E. neither a profit nor a loss

My original answer was E. I cant seem to find why its wrong. Thanks.

This problem is restricted to positive integers, so if you're not so comfortable with algebra, you could guess and check the original cost of each stock.

Cheaper stock:
Cost < 96, selling price = 96.
If cost = 90, then profit = .2*90 = 18 and selling price = 90+18 = 108. Too big.
If cost = 80, then profit = .2*80 = 16 and selling price = 80+16 = 96. Success!

More expensive stock:
Cost > 96, selling price = 96.
If cost = 110, then loss = .2*110 = 22 and selling price = 110-22 = 88. Too small.
If cost = 120, then loss = .2*120 = 24 and selling price = 120-24 = 96. Success!

Thus:
Total cost = 80 + 120 = 200.
Total of selling prices = 2*96 = 192.
Difference = 200-192 = 8 dollars loss.

The correct answer is C.