If a trader, by means of false measures, gains 20% while buy : GMAT Problem Solving (PS)
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# If a trader, by means of false measures, gains 20% while buy

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Manager
Joined: 25 Aug 2011
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03 Nov 2011, 08:57
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If a trader, by means of false measures, gains 20% while buying and again gains 25% while selling. What is his overall gain%

[Reveal] Spoiler:
50%.
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03 Nov 2011, 10:09
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Assume that the cost price of the item is x. Then the trader pays x(1-20/100) = 0.8x for it. Therefore gain made in buying the item = x - 0.8x = 0.2x
Next, he sells it for a 25% gain. So he sells it at 0.8x(1+25/100) = x. Gain made while selling = x - 0.8x = 0.2x

Total gain = 0.2x + 0.2x = 0.4x
Cost price = 0.8x
Therefore % gain = 0.4x/0.8x = 50%
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03 Nov 2011, 10:40
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Manager
Joined: 25 Aug 2011
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03 Nov 2011, 11:25
kostyan5 wrote:

The logic i was using was as follows :

original Price (OP) was 100 units @ 1/- . OP= 100/-
Buying price - 120 units for 100/- (he used false measures, hence reducing the quantitiy and not the amount)
selling price - 90 units for 100/-
Gain = SP-BP = (100/90) - (100/120) = 10/36
Gain% is gain/BP = (10/36)/(100/90) = 25%

What is wrong with what I am doing ?Thanks in advance
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03 Nov 2011, 22:41
devinawilliam83 wrote:
kostyan5 wrote:

The logic i was using was as follows :

original Price (OP) was 100 units @ 1/- . OP= 100/-
Buying price - 120 units for 100/- (he used false measures, hence reducing the quantitiy and not the amount)
selling price - 90 units for 100/-
Gain = SP-BP = (100/90) - (100/120) = 10/36
Gain% is gain/BP = (10/36)/(100/90) = 25%

What is wrong with what I am doing ?Thanks in advance

I will tell you the direct method of doing this but first let me explain what's wrong with your method.
Remember that the gain is in terms of money, not in terms of units.

original Price (OP) was 100 units @ 1/- . OP= $100/- Buying price - 120 units for$100/- (he used false measures, hence reducing the quantitiy and not the amount)
The value of 120 units is $120 so his gain is$20/$100 = 25% selling price - 90 units for 100/- Gain = SP-BP = (100/90) - (100/120) = 10/36 Gain% is gain/BP = (10/36)/(100/90) = 25% When he sells, he gains 25% by using false measures. For$100, he should have given the customer 100 units but he gives only 80 units to get a 25% gain.
His cost price of 80 units is $80 and selling price is$100 so gain = 20/80 * 100 = 25%

So he sells 80 units for $100 He will sell 120 units for$(100/80) * 120 = $150 How much did he pay for these 120 units? Only$100 (again because he used false measures)
Gain = (50/100) *100= 50%

You can also do this directly. There are 2 consecutive gains -> 20% and 25%
Overall gain = a + b + ab/100 = 20 + 25 + 20*25/100 = 50%
To check out how we arrive at this formula, see: http://www.veritasprep.com/blog/2011/02 ... e-changes/
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 25 Aug 2011 Posts: 193 Location: India GMAT 1: 730 Q49 V40 WE: Operations (Insurance) Followers: 1 Kudos [?]: 300 [0], given: 11 Re: Profit and loss [#permalink] ### Show Tags 04 Nov 2011, 04:51 VeritasPrepKarishma wrote: devinawilliam83 wrote: kostyan5 wrote: Assume trader started with X amount of money. After buying, he had 1.2X. After selling he had 1.25(1.2X) = 1.5X. So he made 50%. The logic i was using was as follows : original Price (OP) was 100 units @ 1/- . OP= 100/- Buying price - 120 units for 100/- (he used false measures, hence reducing the quantitiy and not the amount) selling price - 90 units for 100/- Gain = SP-BP = (100/90) - (100/120) = 10/36 Gain% is gain/BP = (10/36)/(100/90) = 25% What is wrong with what I am doing ?Thanks in advance I will tell you the direct method of doing this but first let me explain what's wrong with your method. Remember that the gain is in terms of money, not in terms of units. original Price (OP) was 100 units @ 1/- . OP=$100/-
Buying price - 120 units for $100/- (he used false measures, hence reducing the quantitiy and not the amount) The value of 120 units is$120 so his gain is $20/$100 = 25%

selling price - 90 units for 100/-
Gain = SP-BP = (100/90) - (100/120) = 10/36
Gain% is gain/BP = (10/36)/(100/90) = 25%

When he sells, he gains 25% by using false measures.
For $100, he should have given the customer 100 units but he gives only 80 units to get a 25% gain. His cost price of 80 units is$80 and selling price is $100 so gain = 20/80 * 100 = 25% So he sells 80 units for$100
He will sell 120 units for $(100/80) * 120 =$150

How much did he pay for these 120 units? Only $100 (again because he used false measures) Gain = (50/100) *100= 50% You can also do this directly. There are 2 consecutive gains -> 20% and 25% Overall gain = a + b + ab/100 = 20 + 25 + 20*25/100 = 50% To check out how we arrive at this formula, see: http://www.veritasprep.com/blog/2011/02 ... e-changes/ That was really helpful Karishma, Thanks s ton for this Manager Status: livin on a prayer!! Joined: 12 May 2011 Posts: 124 Location: Australia Followers: 0 Kudos [?]: 32 [0], given: 1 Re: Profit and loss [#permalink] ### Show Tags 04 Nov 2011, 18:37 You can also put in a SMART number. Let the number be 100. 20% of 100 = 20, so price is 120. 25% of 120 is 30, so price is 150 Therefore there is a change of 50 units from 100 = 50% _________________ Aim for the sky! (800 in this case) If you like my post, please give me Kudos Senior Manager Status: mba here i come! Joined: 07 Aug 2011 Posts: 270 Followers: 43 Kudos [?]: 1067 [0], given: 48 Re: Profit and loss [#permalink] ### Show Tags 08 Nov 2011, 02:46 1.2*1.25 = 1.5 so 50% _________________ press +1 Kudos to appreciate posts Re: Profit and loss [#permalink] 08 Nov 2011, 02:46 Similar topics Replies Last post Similar Topics: 3 Listed below are the mean temperatures measured in the Tokha 5 11 Jul 2013, 03:23 2 A milk vendor sells milk at Cost Price but still gains 20%. 2 28 Oct 2012, 20:48 33 A man cheats while buying as well as while selling. While 18 01 Jul 2012, 21:02 25 A wall clock gains 2 mins in 12 hrs, while a table clock 20 31 Aug 2010, 05:43 14 A man sold 20 articles for$60 and gained 20%. How many 11 28 Jul 2010, 08:20
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# If a trader, by means of false measures, gains 20% while buy

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