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# A man cheats while buying as well as while selling. While

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A man cheats while buying as well as while selling. While [#permalink]

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01 Jul 2012, 22:02
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Responding to a pm:

A man cheats while buying as well as while selling. While buying he takes 10% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 9.09% below the cost price of the claimed weight.

Options:

A. 19.81%

B. 20%

C. 37.5%

D. 25%

E. 37.5%

In weight questions, try to go one step at a time.
Say the man buys 100 pounds for $100. But he cheats and takes 110 pounds. This means HIS cost price is$10/11 per pound.
While giving 100 pounds, he actually gives only 80 pounds and charges 9.09% less i.e. 1/11 less than the cost price of 100 pounds which is $100. So he sells at 10/11 * 100 = 1000/11 HIS cost price for 80 pounds = 10/11 * 80 = 800/11 HIS selling price for 80 pounds = 1000/11 Profit = (1000/11 - 800/11)/800/11 * 100 = 25% [Reveal] Spoiler: OA _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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01 Jul 2012, 22:02
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There is a one step calculation method too. It requires more thought but is faster.
The man takes 10% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 110 pounds for which he will take from the customer$110. Hence, in effect, there is a 10% mark up.
While selling, he sells 20% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 80 pounds and should have got only$80 for it. So this is again a mark up of $20 on$80 which is 25%.
But he also sells at 9.09% less i.e. gives a discount of 1/11.

(1 + m1%)(1 + m2%)(1 - d%) = (1 + p%)
11/10 * 5/4 * 10/11 = (1 + p%)
profit % = 25%

To understand this formula, see: http://www.veritasprep.com/blog/2011/02 ... nt-profit/
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Senior Manager Joined: 01 Nov 2010 Posts: 289 Location: India Concentration: Technology, Marketing GMAT Date: 08-27-2012 GPA: 3.8 WE: Marketing (Manufacturing) Followers: 10 Kudos [?]: 80 [0], given: 44 Re: Incorrect Weights [#permalink] ### Show Tags 01 Jul 2012, 22:35 second approach seems to be easy after reading your blog post. i am still having a hard time while trying to understnad this line 'While giving 100 pounds, he actually gives only 80 pounds and charges 9.09% less i.e. 1/11 less than the cost price of 100 pounds which is$100. '
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01 Jul 2012, 22:49
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321kumarsushant wrote:
i am still having a hard time while trying to understnad this line
'While giving 100 pounds, he actually gives only 80 pounds and charges 9.09% less i.e. 1/11 less than the cost price of 100 pounds which is $100. ' The man claims he is giving you 100 pounds i.e. selling you 100 pounds of product. He is supposedly giving a discount of 9.09% i.e. charging 1/11 less than the cost price of 100 pounds which is$100. So he is charging only 10/11 of $100 =$1000/11 from you for giving you "100 pounds". But actually, by cheating, he gave you only 80 pounds. So he charged you $1000/11 for 80 pounds. Think of a fruit vendor you go to to buy some peaches. He says the cost price of the peaches is$1 per pound. But he is willing to give you a discount of 9.09%. But instead of 100 pounds of peaches, he weighs only 80 pounds and gives you less. Though he charges you for 100 pounds. How much does he charge?
9.09% less than 100 pounds i.e. 1/11 less than 100 pounds i.e. 10/11 * 100 pounds = 1000/11

Check out this post for conversion of percentages to fractions: http://www.veritasprep.com/blog/2011/02 ... rcentages/
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews GMAT Club Legend Joined: 09 Sep 2013 Posts: 15427 Followers: 649 Kudos [?]: 207 [0], given: 0 Re: A man cheats while buying as well as while selling. While [#permalink] ### Show Tags 18 Jun 2014, 05:03 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Intern Joined: 22 Feb 2014 Posts: 30 Followers: 0 Kudos [?]: 11 [0], given: 14 Re: A man cheats while buying as well as while selling. While [#permalink] ### Show Tags 24 Jul 2014, 11:18 VeritasPrepKarishma wrote: There is a one step calculation method too. It requires more thought but is faster. The man takes 10% more than what he pays for. So if he claims to take 100 pounds, he pays$100 but he actually takes 110 pounds for which he will take from the customer $110. Hence, in effect, there is a 10% mark up. While selling, he sells 20% less. This means, he claims to sell 100 pounds and gets$100 but actually sells only 80 pounds and should have got only $80 for it. So this is again a mark up of$20 on $80 which is 25%. But he also sells at 9.09% less i.e. gives a discount of 1/11. (1 + m1%)(1 + m2%)(1 - d%) = (1 + p%) 11/10 * 5/4 * 10/11 = (1 + p%) profit % = 25% To understand this formula, see: http://www.veritasprep.com/blog/2011/02 ... nt-profit/ Hi How you got 1/11???highlighted part??? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7372 Location: Pune, India Followers: 2286 Kudos [?]: 15097 [1] , given: 224 Re: A man cheats while buying as well as while selling. While [#permalink] ### Show Tags 24 Jul 2014, 20:53 1 This post received KUDOS Expert's post GGMAT760 wrote: VeritasPrepKarishma wrote: There is a one step calculation method too. It requires more thought but is faster. The man takes 10% more than what he pays for. So if he claims to take 100 pounds, he pays$100 but he actually takes 110 pounds for which he will take from the customer $110. Hence, in effect, there is a 10% mark up. While selling, he sells 20% less. This means, he claims to sell 100 pounds and gets$100 but actually sells only 80 pounds and should have got only $80 for it. So this is again a mark up of$20 on $80 which is 25%. But he also sells at 9.09% less i.e. gives a discount of 1/11. (1 + m1%)(1 + m2%)(1 - d%) = (1 + p%) 11/10 * 5/4 * 10/11 = (1 + p%) profit % = 25% To understand this formula, see: http://www.veritasprep.com/blog/2011/02 ... nt-profit/ Hi How you got 1/11???highlighted part??? This is given in the question: "if he sells at 9.09% below the cost price of the claimed weight." 9.09% written in fraction form is 9.09/100 = 1/11 You should know the basic percentage to fraction conversions given here: http://www.veritasprep.com/blog/2011/02 ... rcentages/ _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: A man cheats while buying as well as while selling. While [#permalink]

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25 Jul 2014, 02:09
VeritasPrepKarishma wrote:
GGMAT760 wrote:
VeritasPrepKarishma wrote:
There is a one step calculation method too. It requires more thought but is faster.
The man takes 10% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 110 pounds for which he will take from the customer$110. Hence, in effect, there is a 10% mark up.
While selling, he sells 20% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 80 pounds and should have got only$80 for it. So this is again a mark up of $20 on$80 which is 25%.
But he also sells at 9.09% less i.e. gives a discount of 1/11.
(1 + m1%)(1 + m2%)(1 - d%) = (1 + p%)
11/10 * 5/4 * 10/11 = (1 + p%)
profit % = 25%

To understand this formula, see: http://www.veritasprep.com/blog/2011/02 ... nt-profit/

Hi

How you got 1/11???highlighted part???

This is given in the question:
"if he sells at 9.09% below the cost price of the claimed weight."

9.09% written in fraction form is 9.09/100 = 1/11

You should know the basic percentage to fraction conversions given here: http://www.veritasprep.com/blog/2011/02 ... rcentages/

Needless to say its a good question

9.09% = 1/11 .... This approximation makes the life easier to compute; else it was not easy to calculate

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Re: A man cheats while buying as well as while selling. While [#permalink]

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02 Jul 2015, 06:48
Hi Bunuel,

Could you please show any easier way of solving this question ?

Thanks.
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Re: A man cheats while buying as well as while selling. While [#permalink]

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02 Jul 2015, 06:54
Swaroopdev wrote:
Hi Bunuel,

Could you please show any easier way of solving this question ?

Thanks.

There are perfect solutions from Karishma above. Please go through them and ask if anything remains unclear.
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Re: A man cheats while buying as well as while selling. While [#permalink]

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08 Oct 2015, 04:27
VeritasPrepKarishma wrote:
There is a one step calculation method too. It requires more thought but is faster.
The man takes 10% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 110 pounds for which he will take from the customer$110. Hence, in effect, there is a 10% mark up.
While selling, he sells 20% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 80 pounds and should have got only$80 for it. So this is again a mark up of $20 on$80 which is 25%.
But he also sells at 9.09% less i.e. gives a discount of 1/11.

(1 + m1%)(1 + m2%)(1 - d%) = (1 + p%)
11/10 * 5/4 * 10/11 = (1 + p%)
profit % = 25%

To understand this formula, see: http://www.veritasprep.com/blog/2011/02 ... nt-profit/

can you please clear about (1+m2)= 5/4?? i can not understand fro m where did u get this.
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Re: A man cheats while buying as well as while selling. While [#permalink]

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08 Oct 2015, 21:43
anik19890 wrote:
VeritasPrepKarishma wrote:
There is a one step calculation method too. It requires more thought but is faster.
The man takes 10% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 110 pounds for which he will take from the customer$110. Hence, in effect, there is a 10% mark up.
While selling, he sells 20% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 80 pounds and should have got only$80 for it. So this is again a mark up of $20 on$80 which is 25%.
But he also sells at 9.09% less i.e. gives a discount of 1/11.

(1 + m1%)(1 + m2%)(1 - d%) = (1 + p%)
11/10 * 5/4 * 10/11 = (1 + p%)
profit % = 25%

To understand this formula, see: http://www.veritasprep.com/blog/2011/02 ... nt-profit/

can you please clear about (1+m2)= 5/4?? i can not understand fro m where did u get this.

There are two mark ups in this question -
the first mark up of 10% (he takes 110 pounds for which he will get $110 though he pays only$100 for it - that is a 10% mark up) - this gives you 1 + 10/100 = 11/10
the second mark up of 25% (he gives only 80 pounds for which he had paid $80 but charges$100 for it - the markup of $20 on$80 cost price is a 25% mark up) - this gives you (1 + 25/100) = 5/4
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews GMAT Club Legend Joined: 09 Sep 2013 Posts: 15427 Followers: 649 Kudos [?]: 207 [0], given: 0 Re: A man cheats while buying as well as while selling. While [#permalink] ### Show Tags 25 Oct 2016, 10:25 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Intern Joined: 07 Jun 2015 Posts: 8 Followers: 0 Kudos [?]: 1 [0], given: 6 Re: A man cheats while buying as well as while selling. While [#permalink] ### Show Tags 27 Oct 2016, 07:54 Hi Karishma, Appreciate your thoughts on my approach. Let Actual cp=100 Cheated cost price – 110 [ 10% more] Selling price – 1000/11 [9.09 % less] Actual selling price – 80 [20% less than actual] Overall profit = 10[110-100]+120/11 [1000/11-80] =230/11 Profit -230/11, cp-100 => profit % = 20.9 approx 21% what's wrong in my approach. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7372 Location: Pune, India Followers: 2286 Kudos [?]: 15097 [0], given: 224 Re: A man cheats while buying as well as while selling. While [#permalink] ### Show Tags 27 Oct 2016, 22:44 SriramK wrote: Hi Karishma, Appreciate your thoughts on my approach. Let Actual cp=100 Cheated cost price – 110 [ 10% more] Selling price – 1000/11 [9.09 % less] Actual selling price – 80 [20% less than actual] Overall profit = 10[110-100]+120/11 [1000/11-80] =230/11 Profit -230/11, cp-100 => profit % = 20.9 approx 21% what's wrong in my approach. The question says that he takes 10% more than what he pays for. This means that if he pays$100 for 100 gms, but takes 110 gms instead.
So the cost price is actually 100/110 per gram = $90.9 per 100 gms Cheated cost price is not 110. It is 90.9 Similarly, think about selling price too. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: A man cheats while buying as well as while selling. While [#permalink]

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13 Nov 2016, 13:45
[quote="VeritasPrepKarishma"]Responding to a pm:

A man cheats while buying as well as while selling. While buying he takes 10% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 9.09% below the cost price of the claimed weight.

Options:

A. 19.81%

B. 20%

C. 37.5%

D. 25%

E. 37.5%

he makes a profit on buying and a profit from selling and he gives a fake discount

100%-1000/11% = 100/11% = 9.09% approx

profit on selling ( form cheating) by decreasing weight by 20%

125%-100% = 25%

fake discount = -9.09% on the deceiving cost of 1

sum the above 3 we get 25%
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Re: A man cheats while buying as well as while selling. While [#permalink]

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21 Jan 2017, 19:12
VeritasPrepKarishma wrote:
Responding to a pm:

A man cheats while buying as well as while selling. While buying he takes 10% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 9.09% below the cost price of the claimed weight.

Options:

A. 19.81%

B. 20%

C. 37.5%

D. 25%

E. 37.5%

In weight questions, try to go one step at a time.
Say the man buys 100 pounds for $100. But he cheats and takes 110 pounds. This means HIS cost price is$10/11 per pound.
While giving 100 pounds, he actually gives only 80 pounds and charges 9.09% less i.e. 1/11 less than the cost price of 100 pounds which is $100. So he sells at 10/11 * 100 = 1000/11 HIS cost price for 80 pounds = 10/11 * 80 = 800/11 HIS selling price for 80 pounds = 1000/11 Profit = (1000/11 - 800/11)/800/11 * 100 = 25% Option C and E are the same. You should edit them. Manager Joined: 01 Mar 2015 Posts: 63 Location: India Concentration: Entrepreneurship, International Business GMAT 1: 690 Q42 V42 Followers: 0 Kudos [?]: 15 [0], given: 6 Re: A man cheats while buying as well as while selling. While [#permalink] ### Show Tags 21 Jan 2017, 23:40 It helps to know the fractional equivalents. One can then proceed by taking convenient numbers. So, say the man paid for 1000 units and got 1100 units. His CP=10/11. Now he claims to sell 1100 units but only sells 880 units (20% less) and at a price 1/11th less (9.09%). So his SP is 1000, while he's incurring a cost of 880*10/11=800. So his overall profit= (1000-800)/800=1/4=25%. _________________ In the pursuit of a better GMAT score. You can help me by giving me kudos if you like my post. Intern Joined: 04 Jan 2015 Posts: 9 Followers: 0 Kudos [?]: 0 [0], given: 2 Re: A man cheats while buying as well as while selling. While [#permalink] ### Show Tags 17 Feb 2017, 16:15 th23autolink_encode_start_318yq1msW3VybD1odHRwcyYjNTg7Ly9nbWF0Y2x1YiYjNDY7Y29tJiM1ODs0NDMvZm9ydW0vbWVtYmVybGlzdCYjNDY7cGhwP21vZGU9dmlld3Byb2ZpbGUmYW1wO3VuPVZlcml0YXNQcmVwS2FyaXNobWE6MzE4eXExbXNdIHRoMjNhdXRvbGlua19iYmNvZGVfc3RhcnRfYl8zMTh5cTFtcyBWZXJpdGFzUHJlcEthcmlzaG1hIHRoMjNhdXRvbGlua19iYmNvZGVfZW5kX2JfMzE4eXExbXMgWy91cmw6MzE4eXExbXNdth23autolink_encode_end_318yq1ms wrote: Responding to a pm: A man cheats while buying as well as while selling. While buying he takes 10% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 9.09% below the cost price of the claimed weight. Options: A. 19.81% B. 20% C. 37.5% D. 25% E. 37.5% In weight questions, try to go one step at a time. Say the man buys 100 pounds for$100. But he cheats and takes 110 pounds. This means HIS cost price is $10/11 per pound. While giving 100 pounds, he actually gives only 80 pounds and charges 9.09% less i.e. 1/11 less than the cost price of 100 pounds which is$100. So he sells at 10/11 * 100 = 1000/11
HIS cost price for 80 pounds = 10/11 * 80 = 800/11
HIS selling price for 80 pounds = 1000/11

Profit = (1000/11 - 800/11)/800/11 * 100 = 25%

Hi VeritasPrepKarishma ,

As I have understood , you got the man's REAL cost price i.e 10/11 per pound .

His Cost price for 80 kgs = 80 * 10/11
But his selling price for 80ks = 100 * 10/11 ( because he says its not 80 its hundred) .

And then you have calculated the difference . Where does the 9.09% factor in ?

shouldnt his selling price be = 100*10/11 - 9.09% [ 100*10/11] . which is not 100*10/11 . therefore changing the answer.

I spent quite a lot of time to understand this, any help will be appreciated.
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A man cheats while buying as well as while selling. While [#permalink]

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26 Feb 2017, 21:13
See it this way

what he pays for - 100 gm
what he actually gets - 110 gm

when merchant sells
what he charges for - 100 gm
what he gives - 80 gm of material

So in a single transaction he buys 110 gm for a certain amount and sells 80 for the same amount.
The difference 110-80 is what accounts for his profit.
This is without considering the discount he gives

Now if i consider the discount also
discount is 9.09%

suppose cost per unit is X

for 91x he sold 80 gm
for 100x he will sell (80/91) * 100 = 88gm

So he bought 110 gm for certain amount and sold 88 gm for the same amount so his net gain is 110-88 =22gm
so for 88 gm sold he made 22gm profit

profit = 22/88 * 100 = 25%
A man cheats while buying as well as while selling. While   [#permalink] 26 Feb 2017, 21:13

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