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# A shopkeeper has 280 kg of apples. He sells 40% of these at 20% profit

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Math Expert
Joined: 02 Aug 2009
Posts: 5909
A shopkeeper has 280 kg of apples. He sells 40% of these at 20% profit [#permalink]

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26 Mar 2016, 04:43
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45% (medium)

Question Stats:

69% (01:39) correct 31% (01:54) wrong based on 276 sessions

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A shopkeeper has 280 kg of apples. He sells 40% of these at 20% profit and remaining 60% at 30% profit. Find his % profit on total.

A. 24%
B. 25%
C. 26%
D. 28%
E. 35%

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Re: A shopkeeper has 280 kg of apples. He sells 40% of these at 20% profit [#permalink]

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26 Mar 2016, 05:03
1
Total number of apples = 280

Let the cost price be x
Selling price at 20% profit = 1.2x
Selling price at 30% profit = 1.3x

Profit % = ((SP - CP)/CP)*100

Profit % = ((2/5)*280*1.2x + (3/5)*280*1.3x - 280x)/280x * 100 = (1/5*(2.4 + 3.9) - 1)*100
= (6.3 - 5)*20 = 26%

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Re: A shopkeeper has 280 kg of apples. He sells 40% of these at 20% profit [#permalink]

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26 Mar 2016, 05:55
2
4
Vyshak wrote:
Total number of apples = 280

Let the cost price be x
Selling price at 20% profit = 1.2x
Selling price at 30% profit = 1.3x

Profit % = ((SP - CP)/CP)*100

Profit % = ((2/5)*280*1.2x + (3/5)*280*1.3x - 280x)/280x * 100 = (1/5*(2.4 + 3.9) - 1)*100
= (6.3 - 5)*20 = 26\%

Perhaps 280 kg of apples is not a necessary information, since you can reach the same result in this way

$$20\%\cdot 40\%+30\%\cdot60\%=26\%$$
Math Expert
Joined: 02 Aug 2009
Posts: 5909
Re: A shopkeeper has 280 kg of apples. He sells 40% of these at 20% profit [#permalink]

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26 Mar 2016, 06:06
2
1
Vyshak wrote:
Total number of apples = 280

Let the cost price be x
Selling price at 20% profit = 1.2x
Selling price at 30% profit = 1.3x

Profit % = ((SP - CP)/CP)*100

Profit % = ((2/5)*280*1.2x + (3/5)*280*1.3x - 280x)/280x * 100 = (1/5*(2.4 + 3.9) - 1)*100
= (6.3 - 5)*20 = 26%

Hi,

ngie is absolutely correct, I had written 280 just to ensure that you spend some time on it..
Always be careful on what is required..

This Q if done by weighted average method
20% profit on 40% items or $$\frac{4}{10}$$ items
30% profit on 60% items.. or $$\frac{6}{10}$$ items

so average =$$20 + \frac{6}{10}*(30-20)= 26$$
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Re: A shopkeeper has 280 kg of apples. He sells 40% of these at 20% profit [#permalink]

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19 May 2016, 09:36
chetan2u wrote:
Vyshak wrote:
Total number of apples = 280

Let the cost price be x
Selling price at 20% profit = 1.2x
Selling price at 30% profit = 1.3x

Profit % = ((SP - CP)/CP)*100

Profit % = ((2/5)*280*1.2x + (3/5)*280*1.3x - 280x)/280x * 100 = (1/5*(2.4 + 3.9) - 1)*100
= (6.3 - 5)*20 = 26%

Hi,

ngie is absolutely correct, I had written 280 just to ensure that you spend some time on it..
Always be careful on what is required..

This Q if done by weighted average method
20% profit on 40% items or $$\frac{4}{10}$$ items
30% profit on 60% items.. or $$\frac{6}{10}$$ items

so average =$$20 + \frac{6}{10}*(30-20)= 26$$

This might sound stupid, but can you please let me know how you arrived to this step? average =$$20 + \frac{6}{10}*(30-20)= 26$$ ?
Math Expert
Joined: 02 Aug 2009
Posts: 5909
Re: A shopkeeper has 280 kg of apples. He sells 40% of these at 20% profit [#permalink]

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19 May 2016, 09:50
1
powellmittra wrote:
chetan2u wrote:
Vyshak wrote:
Total number of apples = 280

Let the cost price be x
Selling price at 20% profit = 1.2x
Selling price at 30% profit = 1.3x

Profit % = ((SP - CP)/CP)*100

Profit % = ((2/5)*280*1.2x + (3/5)*280*1.3x - 280x)/280x * 100 = (1/5*(2.4 + 3.9) - 1)*100
= (6.3 - 5)*20 = 26%

ngie is absolutely correct, I had written 280 just to ensure that you spend some time on it..
Always be careful on what is required..

This Q if done by weighted average method
20% profit on 40% items or $$\frac{4}{10}$$ items
30% profit on 60% items.. or $$\frac{6}{10}$$ items

so average =$$20 + \frac{6}{10}*(30-20)= 26$$

This might sound stupid, but can you please let me know how you arrived to this step? average =$$20 + \frac{6}{10}*(30-20)= 26$$ ?

Hi powellmittra,
No Q is stupid and this in any case is a very genuine Q..
I have used here Weighted average method or Alligation method...
It means that the average of any two mixtures is dependent on the ratio of their quantity..
It is very useful in mixtures and averages Q, if mastered..

here we have 20 % and 30% and average has to be between these two and it will depend on their quantity...
20% has 40% quantity and 0% has 60% quantity, so average will be closer to 30 as the quantity of 30% is more..

by weighted average method
20% profit on 40% items or $$\frac{4}{10}$$ items
30% profit on 60% items.. or $$\frac{6}{10}$$ items

so average =$$20 + \frac{6}{10}*(30-20)= 26$$..
we are dividing the 30-20 = 10 in these 100 parts and then divide them in 60:40 ....
so 20%:30% = 40:60.....
so average will be 60/100 *10 away from 20 OR
40/100 * 10 less than 30..
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Re: A shopkeeper has 280 kg of apples. He sells 40% of these at 20% profit [#permalink]

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19 May 2016, 10:07
1
1
If the total quantity was 100

Then 40X 20% + 60 X30%= 26

This profit will remain same for any total quantity unless the % of products remains the same. Hence 'C' is the answer
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Re: A shopkeeper has 280 kg of apples. He sells 40% of these at 20% profit [#permalink]

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09 Aug 2017, 13:29
The 280 kg of apple really threw me off. I figured half way through my time that it was useless bit of information and chose to roll with the number 100 to make life easier. It works out the same way, though, in my experience, you will still get it wrong if you don't do the basic math skills.
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A shopkeeper has 280 kg of apples. He sells 40% of these at 20% profit [#permalink]

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10 Aug 2017, 09:44
1
chetan2u wrote:
A shopkeeper has 280 kg of apples. He sells 40% of these at 20% profit and remaining 60% at 30% profit. Find his % profit on total.

A. 24%
B. 25%
C. 26%
D. 28%
E. 35%

For me, intuitively, it's easier to think about profit as some original 1 plus percent profit.

(.4)(1.2) + (.6)(1.3)

.48 + .78 = 1.26

Percent profit =
change/original * 100

$$\frac{(1.26-1)}{1}$$ = .26*100 = 26%

But I worry: have I confused markup with profit?
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Re: A shopkeeper has 280 kg of apples. He sells 40% of these at 20% profit [#permalink]

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29 Sep 2017, 15:41
genxer123 wrote:
But I worry: have I confused markup with profit?

Aren't the two terms Markup and Profit interchangeable?
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Re: A shopkeeper has 280 kg of apples. He sells 40% of these at 20% profit [#permalink]

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20 Nov 2017, 17:46
chetan2u wrote:
A shopkeeper has 280 kg of apples. He sells 40% of these at 20% profit and remaining 60% at 30% profit. Find his % profit on total.

A. 24%
B. 25%
C. 26%
D. 28%
E. 35%

hi

w1/w2 = 40/60
or, 2/3

now,

20 * 2 + 30 * 3
_____________
5

= 26

thanks
cheers through the kudos button if this helps
Re: A shopkeeper has 280 kg of apples. He sells 40% of these at 20% profit   [#permalink] 20 Nov 2017, 17:46
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