A man cheats while buying as well as while selling. While : Problem Solving (PS)

321kumarsushant

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

01 Jul 2012, 22:35

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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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KarishmaB

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

Updated on: 08 Oct 2022, 22:13

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321kumarsushant wrote:

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. '

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

Originally posted by KarishmaB on 01 Jul 2012, 22:49.
Last edited by KarishmaB on 08 Oct 2022, 22:13, edited 1 time in total.

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KarishmaB

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

Updated on: 17 Oct 2022, 00:56

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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: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/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

Originally posted by KarishmaB on 24 Jul 2014, 20:53.
Last edited by KarishmaB on 17 Oct 2022, 00:56, edited 1 time in total.

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KarishmaB

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

26 May 2017, 01:31

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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: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/02 ... nt-profit/

Responding to a pm:

Quote:

can u please clear me ..what if the question will ask for his Profit/loss percent"??

ie how can we know whether he is finally at profit or loss so that we have RHS part as (1+p%)

In case there is a loss, you will simply get a negative value for p.

(1 + m%)(1 - d%) = (1 + p%)

Say there is a mark up of 10% but a discount is given of 20%.

(1 + 10/100)*(1 - 20/100) = (1 + p%)

(11/10) * (4/5) = (1 + p%)

44/50 = 88/100 = 1 + p/100

p/100 = -12/100

p = -12

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vipultodev

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

12 May 2020, 02:14

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110/100 * 100/80 * 10/11 = sp/cp = 10/8
profit % = 2/8 = 25%

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

22 Jul 2021, 13:52

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VeritasKarishma 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%

If anyone is uncomfortable with Fractions.

You see 20 % then you should understand 80% of x

Hence, take such num's as 80 Units, 10 per unit ;$ 80*10 = 800 = C.P $

He gets 10% Extra : He gets 88 units.

Now he sells 20% less. that means he SAYS he is giving 10 units and gives 8

so No of units he can sell = 88*10/8 = 110

he sells at 9.09 lesser than CP .
CP/unit = 10 , SP/unit = 9.1 ( Options A, B are so close that rounding off looks risky )

so he sells 110 units at 9.1 per unit

Total revenue he got 110*9.1 = 999

so profit = $\frac{(999-800 )*100}{ 800}$ = 25%

Or else,

sp/cp = $110/100*100/80*10/11= 10/8$

Profit % = $\frac{2}{8}$

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

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: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/02 ... nt-profit/

Hi

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

anik19890

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

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: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/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]

08 Oct 2015, 21:43

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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: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/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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SriramK

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

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.

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

27 Oct 2016, 22:44

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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.

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

01 Dec 2022, 18:20

I found the explanation of a similar question very helpful:
a-merchant-claims-a-loss-of-4-on-coffee-but-uses-a-weight-of-840-gms (sorry, not allowed to post urls yet)

So I tried to explain this one in a similar way but got this:
let's say the price of 1000g is 1000 cents
but he gets 1100g for 1000 cents. In that way, basically gained 100 cents for himself
then he sells 800g for 909.1 cents (since 1000 cents - 9.09% discount = 909.1 cents) which he should've sold for 800 cents. In that way, gained 909.1-800 = 109.1 cents for himself
altogether, his cheating got him 209.1 cents
209.1/800 = slightly more than 25% which is not among the answer choices.
Where did I go wrong?

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

07 Jan 2023, 05:17

This is my understanding of the question and my answer is different.

Let's say pound bought is a. And price paid is x. I am only following the money.

His total cost will be ax.

Now in actual sense he took more, in this case 10%. Weight he has to sell is now 1.1a.

He paid for ax items but has 1.1a to sell.

If he cheats his customers by giving them 20% less and 9.09% discount, amount he will make will be

0.2X 1.1 = 0.22

0.22 + 1.1a = 1.32a.

My thinking is if he cheats them by 20% less, he will make 20% more money and a discount of 9.09% will make his selling price to be 0.9091x.

Total amount made will be 1.32 X 0.9091 = 1.200012ax

His profit therefore will be 1.200012ax - ax = 0.200012ax

0.200012ax/ax X 100 = 20%.

Anything wrong here?

Posted from my mobile device

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

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GMAT Problem Solving (PS) Questions

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