John bought 2 shares and sold them 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 John 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

Sold both shares for $96 each, 1 20% profit, 1 20% loss.

96% for 20% profit:
96 = 1.2x
x = 80
96 - 80 = 16 profit

96% for 20% loss:
96 = 0.8x
x = 120
120 - 96 = 24 loss

24 loss - 16 profit = 8 loss.

C.

$ Profit of the share sold at 20% profit =
120-96
20-?
$16 profit on the sale of 1 share.

$ Loss of the share sold at 20% loss=
80-96
20-?
$24 loss on the sale of 1 share.

16-24=Loss of $8

Answer: C

Sold both shares (A+B) for?

96 + 96 = 192

Bought both shares for?

A: 96 / (6/5) = 16 * 5 = 80

B: 96 / (4/5) = 24 * 5 = 120

A + B = 200

Profit: 192 - 200 = -8

Answer: C

for 2 products ,Whenever selling price is same and there is x% profit on one and x% loss on other then there is loss on whole transaction.
Here ,
for first prodcut
96 = 1.2x
x = 80
First Cost price = 80

For second product
96 = 0.8x
x = 120
second cost price=120

total cost price =120+80=200
total selling price = 96+96 =192
Hence , loss of 8$

For the share in profit,

1.2x=96
x=80

for the share in loss,

0.8y=96
y=120

Total C.P = x+y = 120+20=200

Total S.P = 96 *2 = 192

Loss = 200 - 192= $8

Answer C

Cost price of each share=x
Sale price of share A=0.8x
Therefore, 0.8x=96
x=120
Loss=$24
Sale price of share B=1.2X=96
X=80
Profit=16
Net loss=$8
Answer C

VERITAS PREP OFFICIAL SOLUTION

Note that the question would have been straight forward had the COST price been the same, say $100. A 20% profit would mean a gain of $20 and a 20% loss would mean a loss of $20. Overall, there would have been no profit no loss.

Here the two shares are sold at the same SALE price. One at a profit of 20% on cost price which must be lower than the sale price (to get a profit) and the other at a loss of 20% on cost price which must be higher than the sale price (to get a loss). 20% of a lower amount will be less in dollar terms and hence overall, there will be a loss.

The loss % = (20)^2/100 % = 4%.

But we need the amount of loss, not the percentage of loss.

Total Sale price of the two shares = 2*96 = $192

Since there is a loss of 4%, the 96% of the total cost price must be the total sale price

(96/100)*Cost Price = Sale Price

Cost Price = $200

Loss = $200 – $192 = $8

Answer (C)
_________________

total CP = 9600/120 + 9600/80 = 80 + 120=200
SP=96*2=192
loss= Rs 8/-
C

For EQUAL SELLING PRICE and EQUAL %age PROFIT AND LOSS ON ARTICLES the resultant loss or profit is calculated as follows

The situations always lead to loss

Loss% = (%age Profit or loss / 10)^2 = (20/10)^2 = 4% loss

Total Selling Price = 96*2 = $192
Total Cost Price = 192/(0.96) = $200

Loss = 200-192 = $8

Answer: Option C

ALTERNATIVE

Cost price of first share = 96 / 1.2
Cost price of first share = 96 / 0.8

Total Cost price of both shares = (96 / 1.2 )+(96 / 0.8) = $200

Total Loss = 200-192 = $8

Answer: Option C
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For the one share earning a 20% profit, we can set up the following equation in which c = cost:

Profit = 0.2c

96 - c = 0.2c

96 = 1.2c

80 = c

Thus, John made 96 - 80 = 16 dollars on the sale.

For the share with a 20% loss, we can set up the following equation in which c = cost:

Profit = -0.2c

96 - c = -0.2c

96 = 0.8c

120 = c

Thus, John lost 120 - 96 = 24 dollars on the sale.

So, overall he lost 8 dollars.

Answer: C
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Harikamini

Please find answer to your question posted as PM

Since the loss incurred is 4% therefore we can deduce that revenue is only 96% of the cost

i.e. (96/100)*Total Cost = 192

i.e. Total Cost = 192/0/96 = 200

I hope this clears your doubt.
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Hi Chetan,
Your approach is short and sweet and I like it.
Can you solve this problem, just by using conceptual approach? (without using the math I mean)
If it is possible, can you give a try?

Thanks in advance!

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