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If a trader, by means of false measures, gains 20% while buy

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devinawilliam83
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If a trader, by means of false measures, gains 20% while buy [#permalink] New post   03 Nov 2011, 09:57
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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 percentage?

A. 40%
B. 45%
C. 50%
D. 55%
E. 60%
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Re: If a trader, by means of false measures, gains 20% while buy [#permalink] New post   03 Nov 2011, 11:09
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The answer is 50%.

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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Re: If a trader, by means of false measures, gains 20% while buy [#permalink] New post   03 Nov 2011, 11:40
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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%.
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Re: If a trader, by means of false measures, gains 20% while buy [#permalink] New post   03 Nov 2011, 12:25
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
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Re: If a trader, by means of false measures, gains 20% while buy [#permalink] New post   Updated on: 08 Oct 2022, 03:25
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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%

Originally posted by KarishmaB on 03 Nov 2011, 23:41.
Last edited by KarishmaB on 08 Oct 2022, 03:25, edited 1 time in total.
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Re: If a trader, by means of false measures, gains 20% while buy [#permalink] New post   04 Nov 2011, 05:51
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: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/02 ... e-changes/



That was really helpful Karishma, Thanks s ton for this
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Re: If a trader, by means of false measures, gains 20% while buy [#permalink] New post   04 Nov 2011, 19:37
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%
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Re: If a trader, by means of false measures, gains 20% while buy [#permalink] New post   08 Nov 2011, 03:46
1.2*1.25 = 1.5
so 50%
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Re: If a trader, by means of false measures, gains 20% while buy [#permalink] New post   11 Jan 2024, 09:04
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