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

Question

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%

ngie · Accepted Answer

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\%

chetan2u · Answer

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

Kurtosis · Answer

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%

Answer: C

powellmittra · Answer

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  ?

chetan2u · Answer

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..

Divyadisha · Answer

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

pingala · Answer

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.

generis · Answer

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%

Answer C

But I worry: have I confused markup with profit?

Blackbox · Answer

Aren't the two terms Markup and Profit interchangeable?

testcracker · Answer

hi w1/w2 = 40/60 or, 2/3 now, 20 * 2 + 30 * 3 _____________ 5 = 26 thanks cheers through the kudos button if this helps

Manasvi1 · Answer

Let C.P. of 1 kg apples be= x 
Then, C.P. of 280 kg apples= 280x

40% of 280 kg apples= 40% of 280 = (40/100) * 280 = 112 kg
C.P. of 112 kg apples= 112*x= 112x
Profit% on 112 kg apples= 20%
Therefore,
Profit= 20% of 112x = (20/100)*112x = 22.4 x
Remaining apples= 280 kg - 112 kg = 168 kg (60% apples)
C.P. of 112 kg apples= 168*x= 168x
Profit% on 168 kg apples= 30%
therefore,
Profit= 30% of 168x = (30/100)*168x = 50.4 x

Total profit= 50.4x + 22.4x = 72.8x
Total C.P. = 280x
Total profit% =  % =  % = 26%

Hence Option answer choice(C)

navya27 · Answer

Quicker approach:

we can eliminate A,B,E as we know that value will lie between 25 and 30.

Let's say 100% apples were sold at 30% profit, therefore total profit = 30%
if 50% were sold at 20% P and rest 50% apples at 30%, total P would avg. out to be 25% so with every 10% inc in % of apples sold at higher profit, there is 1% inc in profit %.

Therefore at 60% =26% total profit 
70% = 27% total profit
At 80% total profit would be 28%. 
90% = 29% Total profit
100% = 30% total profit

KarishmaB · Answer

For profit%, when we use weighted averages, our weights are cost price. Since no distinction is made between the apples, all apples are assumed to have the same cost price. Hence the ratio of cost price for 20% profit and cost price for 30% profit would be 40:60 (the ratio of the number of apples) Using scale method: Screenshot 2023-08-08 at 7.33.48 PM.png Ratio of weights is 2:3 so distances from average will be in the ratio 3:2. Since total distance between 20% and 30% is 10%, it means average will be 6% away from 20% and 4% behind 30%. Hence average must be 26% Answer (C) Note that the actual total weight of apples is irrelevant. Check Weighted Avg here: https://anaprep.com/arithmetic-weighted-averages/ and this video: https://www.youtube.com/watch?v=_GOAU7moZ2Q

Paras96 · Answer

A shopkeeper has 280 kg of apples. He sells 40% of these at 20% profit and the remaining 60% at 30% profit. Find his % profit on the total.
 Method 1 
Let x be the cost price per kg of apple 
=> Selling price of apples = 40%*280*1.2x + 60%*280*1.3x
=> Selling price of apples = 134.4x+218.4x=352.8x

The cost price of apples = 280x

=>Profit % = (SP - CP)*100/CP
=>Profit % = (352.8 - 280)*100x/280
=>Profit % = 26%

Hence C

Method 2 
By weighted average 
=>Profit % = 40%*20%+60%*30%
=> Profit % = 8% + 18% = 26%
Hence C

bumpbot · Answer

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

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