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Very Simple Percent Question - confused by formula

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Very Simple Percent Question - confused by formula

by AndyXL » Mon Oct 10, 2011 12:47 pm
I'm having a bit of a dumb moment. This is a really simple problem and I know the steps to the answer - but one of the steps is really confusing me!

A store sells a TV for $600. If the store makes a profit of 20% of its cost, what was the cost of the TV to the store.

I know the answer is $500 (and it's easy for me to check the answer by working out 20% of $500).

One of the books I'm using gives me the basic starting formula of: cost + profit = selling price and sets out the following steps:

Step 1: C + 20%C = $600

Step 2: C + 1/5C = $600 (so far so good)!

Step 3: 6/5C = $600 (this is where I lose it - I don't understand the transition between steps 2 and 3 - how can C + 1/5C = 6/5C

Step 4: C = $600 x 5/6 = $500 (this makes sense too).

The only bit I don't get is from Steps 2 to 3. Am I missing something really obvious?

Thanks for any help - it's been a long day and I'm probably being really stupid!
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by shankar.ashwin » Mon Oct 10, 2011 12:55 pm
C + C/5 = 6C/5 (You take LCM and add)

If fractions are confusing, he sells it for 20% profit (20% more than what he bought it for)

120% of C = 600

120/100 * C = 600

C = (600*100)/120 = 500
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by AndyXL » Mon Oct 10, 2011 1:11 pm
Thanks, I knew I was missing something obvious - it's simply adding the fractions together.

Your other method is also helpful :-)

It's going to be a long four months of revision...
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by Whitney Garner » Mon Oct 10, 2011 2:29 pm
AndyXL wrote:The only bit I don't get is from Steps 2 to 3. Am I missing something really obvious
I completely agree with shankar.ashwin in that adding the percents is pretty sweet here, but just to make sure that we can also do this with fractions, here is the reasoning:

C + 1/5C

Remember that the first C could essentially have a 1 in front of it (that's where shankar.ashwin got the 100% from)

So we have 1C + 1/5C.

But to add these things, we need a common denominator - so let's go with 5. I can rewrite 1 as 5/5...

5/5C + 1/5C = (5+1)/5 C = 6/5C.

:)
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by AndyXL » Mon Oct 10, 2011 2:55 pm
Thanks - your explanation on the fraction formula is excellent.

I think having the "C" in the fraction equation confused me, but I can now see clearly how C + 1/5C = 6/5C.
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by GMATGuruNY » Mon Oct 10, 2011 7:10 pm
AndyXL wrote:I'm having a bit of a dumb moment. This is a really simple problem and I know the steps to the answer - but one of the steps is really confusing me!

A store sells a TV for $600. If the store makes a profit of 20% of its cost, what was the cost of the TV to the store.

I know the answer is $500 (and it's easy for me to check the answer by working out 20% of $500).

One of the books I'm using gives me the basic starting formula of: cost + profit = selling price and sets out the following steps:

Step 1: C + 20%C = $600

Step 2: C + 1/5C = $600 (so far so good)!

Step 3: 6/5C = $600 (this is where I lose it - I don't understand the transition between steps 2 and 3 - how can C + 1/5C = 6/5C

Step 4: C = $600 x 5/6 = $500 (this makes sense too).

The only bit I don't get is from Steps 2 to 3. Am I missing something really obvious?

Thanks for any help - it's been a long day and I'm probably being really stupid!
An easy and efficient approach would be to plug in the answer choices, which would represent the cost of the TV.
20% added to the correct answer choice must yield a selling price of 600.

Answer choice: 500
500 + .2(500) = 500+100 = 600.
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by Abhishek009 » Tue Oct 11, 2011 3:37 am
AndyXL wrote:I'm having a bit of a dumb moment. This is a really simple problem and I know the steps to the answer - but one of the steps is really confusing me!

A store sells a TV for $600. If the store makes a profit of 20% of its cost, what was the cost of the TV to the store.

I know the answer is $500 (and it's easy for me to check the answer by working out 20% of $500).
Let the cost of the TV be 100

Profit is 20

So , Selling Price is 120



Now when , selling price is 120 , cost price is 100

when selling price is 1 , cost price is 100/120

when selling price is 600 , cost price is (100/120)*600 =>500 !!!
Abhishek
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by AndyXL » Tue Oct 11, 2011 10:28 am
Thanks for the above replies.

It's amazing how many ways there are to answer a simple question.

What this also shows though is the different thought processes you can go through for each question and if one doesn't work, there's always another method to try :-)
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by ritzzzr » Tue Oct 11, 2011 10:52 am
take C common so it will be
C(1+1/5)cos C is in numerator its not in denominator
now add 1 +1/5=6/5*C

AndyXL wrote:Thanks - your explanation on the fraction formula is excellent.

I think having the "C" in the fraction equation confused me, but I can now see clearly how C + 1/5C = 6/5C.
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by pemdas » Sun Dec 11, 2011 3:20 pm
AndyXL wrote:A store sells a TV for $600. If the store makes a profit of 20% of its cost, what was the cost of the TV to the store.
Hey, this one is very ambiguous question.

A store sells a TV for $600. implies a price of TV @ $600
the store makes a profit of 20% of its cost implies store enjoys profit from sales, i.e. from charging certain price(s). Hereinafter, the ambiguity begins, the cost implied is the cost of store which can be considered a vague reference here. We must make an assumption that the only cost store has is the cost of TV. With this assumption we are set for possible solution.

Cost of TV -> x
Price of TV -> 600
Profit from sales of TV -> x*(100%+20%)

Equation: x*(100%+20%)=600, x=600/120% or x=600/1.2
x=500

p.s. you are digging into unofficial and badly shaped pro-GMAT materials which may be flourishing with such ambiguous details. If you keep on working from these sources, you may demur even what the number system means. Better work towards recognized prep company materials and OGs.
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by cpschott » Mon Dec 12, 2011 9:40 am
having this notation is confusing
C+1/5C looks like C+1/(5C)

should be written more carefully to avoid confusion

C+(1/5)C
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by Elena89 » Mon Dec 12, 2011 11:48 pm
Given: Profit = 20% of Cost
Selling Price = 600

Let Cost = C

Since Profit= (Selling price) - (Cost)

We have 0.2C = 600 - C
=> 1.2C = 600
=> C = 600/1.2
= 500

Answer: $500
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