An investor purchased 100 shares of stock X at 6 1/8 dollars

If the purchase price was 6$ per share then the investor would have made a profit of 300%.

Since the purchase price is slightly more than 6$ the profit would be slightly less than 300%.

Also a 2% brokerage is negligible and it brings down the profit percentage only by a small value. Approximation is very useful to solve these kind of problems as the answer choices are far apart.

Answer: C

HI

there is enough in the choices to get you close to the correct answer..

OPTIONS

A thing of 6 1/8 has become 24...
so profit of <18 on 6 1/8..
clearly it is slightly less than 300%
ans 280%... Brokerage will make a difference of 2-4% which is very negligible..


PROPER METHOD

I. CP — \(6 \frac{1}{8} + \frac{2}{100} \ \ of \ \ 6 \frac{1}{8}=1.02*\frac{49}{8}\)

II. SP — \(24-\frac{2}{100} \ \ of \ \ 24=0.98*24\)

Profit =\(0.98*24-1.02*\frac{49}{8}=\frac{24*98}{100}-\frac{102*49}{100*8}=49*\frac{48*8-102}{800}=49*\frac{282}{800}\)

Profit %=\(100*\frac{49*\frac{282}{800}}{\frac{102*49}{800}}=\frac{100*282}{102}\)=276~280%


C
_________________

Hi
Why many are going wrong is not taking it step wise.
Let us Work on CP and SP separately
CP — 6 1/8 + 2% of 6 1/8=1.02*49/8~50/8=6.25
SP — 24-2%of 24=0.98*24 should be between 23 and 24, say 23.5
Profit =23.5-6.25=17.25
Profit %=100*17.25/6.25=100*1725/(625)=(25*4)(25*69)/(25*25)=4*69=276~280%
_________________

Some simple calculations to be made for this..
buying price = price os total shares+brokerage charges on buy price
=100*49/8 + 2% of (100*49/8)
=624.75$
similarly selling price = 24*100 - 2%of 2400(or u can add this to buy price also)
=2352$
so Profit = SP-CP
=2352-624.75=1727.25$
%= 1727.25/624.75
=2.76 ~ 280%

Ans C

HI

A way I can think of is that the choices will get you close to the correct answer..

A thing of 6 1/8 has become 24...
so profit of <18 on 6 1/8..
clearly it is slightly less than 300%
ans 280%... Brokerage will make a difference of 2-4% which is very negligible..
_________________

Solution 1

100 shares bought for 612.50
Sold 'm for 2400-2%

2% OF 612.50 is easy to calculate. 12.25 ...
2400 minus 2% is also easy to calculate--> 2400/100*2 = 48.
So the profit amounts to 2350-625 (you can approximate here, it won't make much difference): 1725

1725 divided by 625 can be simplified as 69/25, which equals to 2,8.

This can be done within 1.5 minutes.

Solution 2

But if you're in a hurry, you can just see that the 1/8 is negligible and is only there to hand out complex calculations like the one above.

[(2400-48)-(600+12)]/612
=[(2352)-(612)]/612
=1740/612

3 times 612 gives you 1836. Which is 96 more than needed. 96/612 is close to 1/6 (a bit less), which is close to 0.2. So you will need 2 times 612 and 80% of 612 to arrive at 1740. Ans, 280%.

Thanks Mathiaskeul, Its very clear now

cost of selling shares = (24*(98/100)
we multiply by 98, because we loose 2% in brokerage fee reducing our selling price
cost of buying shares = (49/8 * 102/100)
we multiply by 102, because it costs more to buy the shares, when taking the brokerage fee into account

% profit = (selling price/cost price * 100) -1
% profit = (24*98/100) divided by (49/8 * 102/100) * 100 -1
% profit = (24*98/100) * (100*8 / 49*102) * 100 - 1
% profit = (24*98*100*8)/(100*49*102) * 100 -1
% profit = (24*2*8/102) *100 -1
% profit = (192/51)*100 -1
% profit = (3.76 & 100) - 1
= 276%, c is the closest at 280%

Hi all, please let me know if there is something I am not grasping:

Stocks purchased at $6.125.
100% profit on this investment = double the value = $12.50 per stock
200% profit on this investment = triples the value = $18.75 per stock
300% profit on this investment = 4x the original value = $25.00 per stock (roughly)

Therefor profit just below 300% or 280 percent gain (especially after 'fees').

You can do this math in about 30 seconds.

Logic:

If I spend $100 and gain $100, 0% profit on my original investment.
If I spend $100 and gain $150, 50% profit on my original investment.
If I spend $100 and gain $200, 100% profit on my original investment.
If I spend $100 and gain $300, 200% profit on my original investment.


Any critique?

i used approximations...yet i took the longer way...
purchased price let's say is 49/8
100 * 49/8 * 102/100 (2%) -> 49*102/8

selling price:
100*24*98/100 (2% commission fee) - 24*98
24*98/(49*102/8)
24*98*8/49*102
98 is a multiple of 49 -> simplify
24*2*8/102
24*8/51
192/51 -> this is not the end...selling price is 192/51 % greater than the purchase price.
192-51/51 (percent increase) = 141/51 -> we can clearly see that it's less than 300% and clearly more than 200%.
only B and C remain...
to have 300%, we need 153/51. since 141 is close to 153 - we can assume that it's ~280.

C is the answer.

this one was very annoying. I was between B and C. I knew that it is slightly below %300, but couldn't decide if it is below %290. I think autoboat's and mvictor' approaches are good for this type of question.

Since the investor bought and sold the same number (100) of shares of stock X, the percent change in his gain would be the same if he bought and sold 1 share of the stock. Therefore, let’s calculate the percent change on 1 share instead of 100 shares. Since he had to pay 2% commission on purchasing the stock (which means he actually had to pay 102% of the purchase price), his cost on one share is 6 ⅛ x 102/100 = 49/8 x 51/50. Similarly, since he had to pay 2% commission on selling the stock (which means he only received 98% of the selling price), his revenue on one share is 24 x 98/100 = 24 x 49/50.

Therefore, the ratio of the revenue to the cost of 1 share of the stock is:

(24 x 49/50)/(49/8 x 51/50)

24 x 49/50 x 8/49 x 50/51

24 x 1 x 8 x 1/51

192/51

192/51 can be approximated as 190/50 = 3.8 = 380%. That is, the revenue is approximately 380% of the cost. In other words, the profit (or gain) is approximately 280%.

Answer: C
_________________

Let me give away my two cents on this one. This approach didn't take me too much time.

Purchase price \(=\) \(6 \frac{1}{8}\). Since I don't like mixed numbers I quickly transformed it to an improper fraction: \(\frac{49}{8}\).

Purchase price \(*\) quantity of shares \(=\) \(\frac{4900}{8}=\frac{1225}{2}\)

Selling price \(= 24\)

Selling price \(*\) quantity of shares \(= 2400\)

Now let's set up the variation formula:
\(\left(\frac{2400(1.02)}{\frac{1225(1.02)}{2}}-1\right)*100\)

Simplify it:
\(\left(\frac{4800}{1225}-1\right)*100\)

Simplify it further until:
\(\left(\frac{192}{49}-1\right)*100 \rightarrow \left(\frac{143}{49}\right)*100\)

Now, at this stage we now that \(3*49=147\) which is greater than \(143\), so the percent gain is slightly less than \(300\%\). This should be sufficient to select option C; however, if you want more precision, you can try the following multiplication: \(2.5*49=122.5\). Since \(122.5\) is lower than \(143\), we know that the percent gain was greater than \(250\%\). Again, option C is the correct answer.

Hope it helps.

The FASTEST and BEST way to solve such problem with ugly number like this one is to APPROXIMATE!
_________________

The formula for percentage change is:

\(\frac{new}{old}-1\)

\(new=24*.98 \rightarrow 24*\frac{49}{50}\)

\(old=6\frac{1}{8}*1.02 \rightarrow \frac{49}{8}*\frac{51}{50}\)

\(\frac{new}{old}*\frac{8*50}{8*50}=\frac{192*49}{49*51}=\frac{192}{51}=\frac{384}{102}\)

So the approximate percentage gain the investor made is slightly less than \(384\% - 100\% = 284\%\)

Answer C

Hi chetan2u ,

Just a small doubt, wont we add 0.02(24+6) to the denominator?
The first time I solved it , I did so , since I have been applying
Profit% = Total Profit/Total Cost

And I i though brokerage eventually is a cost incurred?

Let me know if my understanding is not correct.

It is mentioned that he paid on both PP and SP!?

Hi chetan2u , I have a doubt -

in the last step of your approach : (24 − 6 1/8 − 0.02(24 + 6 1/8)) / (6 1/8)(24 − 6 1/8 − 0.02 (24 + 6 1/8)) / (6 1/8)


Why have we not divided the whole thing by 6 1/8 + 0.02(24 + 6 1/8) / (6 1/8)(24 − 6 1/8 − 0.02 (24 + 6 1/8) ? Isn't THAT the total cost that has been incurred by the investor? If we do use the mentioned value as the denominator, we'll get a profit of 256% (approx), which is closer to 240% than to 280%. I did it by this method and picked 240%. Could you please let me know where it is that I'm going wrong?

Hi chetan2u

I solved the question and got the profit percentage as 291.8

291.8 is closed to 300 than 280, hence I marked 300 in the answer choice. Can you please guide where I went wrong in my line of reasoning?

Thanks