quants profit and loss

Question

hi all,
I have question below,i am not sure where i am goin wrng with my approach to solve it.

question
A dairy merchant adds 15% water to milk that costs $0.8 per liter and sells milk laced with water at $0.7.what % profit does he make?

My approach

Let there be 100 lits of milk 
then, CP of100 lits of milk =0.8*85=68 (as 15% is water)
SP of 100 lits of milk =0.7*100=70
Therefore profit%= *100=2.94%

which is not the right ans.I want know to wats wrong with my approach,I got few other questions wrong using same approach:(

A)1.66% B)6.25% C)1.25% D)0.625% E)1.667%

nammers · Answer

Milk costs $0.8/litre
When 15% water is added its cost is now $0.8 per 1.15 litre (1 litre milk+ 0.15 litre water)
Per litre cost is:
0.8/1.15=0.69565
Sold for $0.7 so profit is:
0.7-0.69565=$0.435
% profit is cost sold for per litre/ cost per litre:
0.435/0.69565=6.25%

Silver89 · Answer

explained in the second post

ksp · Answer

lets say 100 litres of milk is there.

Cost of 100 litres of milk is $0.80.
Let 15 litres of water be added. 
Now it becomes 115 litres of (milk + water) and its cost is $0.80

Out of which he takes 100 litres and sells it for $0.70.

So 100 litres of it costs (0.8/115)*100 = 0.695

Now the profit made when he sold it for $0.70 is $0.70 - $0.6956 = $0.0044

Now the profit made is (0.0044/0.70)*100 = 0.625.

wontgiveup · Answer

i clearly understand the approach given by others,i just want to know whats wrong if I do the way I did..
@Silver89..can u please tell me where exactly i am making mistake

thanks for the patience

nammers · Answer

You put the cost price as 0.8*85
BUT they are buying 100 litres: 0.8*100 = 80
and then mixing it and selling at 0.7 after mixing it with 15 litres of water (115 litres total)
SO they sell it at 0.7*115 = 80.5
Therefore profit is = 0.5
profit% = 0.5/80 = 6.25%

Hope this helps you.

Silver89 · Answer

your approach is OK but you have a simple mistake ( marked with the red color )
if you have 85 liters of milk and you add to it 15% water, the sum will be 85 + ( 0.15*85 ) = 97.75  NOT 100 
then you can continue with your approach

ksp · Answer

Hi all,

WHich is correct answer.

is it 6.25% or 0.625%

My profit % is for say just the 100litres out of 115
and nammers appraoch is the profit made from the entire 115 litres.

Just the perspective of the question varies slightly. Technically oth are correct and i suppose there is some little more explanation added to the question.

KarishmaB · Answer

Read the first sentence "A dairy merchant adds 15% water to milk that costs $0.8 per liter... " 
He adds 15% water. That means if milk is 100 lts, he adds 15 lts of water to it to make it 115 lts of mixture.

If milk were 85 lts, he will not add 15 lts of water but only 15% of 85 lts of water.

Whenever you have %, focus on % of what? Here you have 15%. This is 15% of the amount of pure milk. He adds 15% of the amount of pure milk. The base is amount of pure milk, not the amount of total mixture.

Now you can easily say the following:
Pure milk = 100 lts
Cost price = .8*100 = $80

Assuming water is free of cost,
Amount of mixture = 115 lts
Selling price = .7*115 = $80.5

Profit % = (80.5 - 80)/80 * 100 = .625% profit

KarishmaB · Answer

Profit is always calculated on the cost price, not the amount of milk/mixture. Both of you have calculated the cost price as $80 and the amount of profit made as $.5.

For both of you, the profit % = .5/80 *100 = .625%
(nammers made a calculation error)

It is a good idea to take an overall review of your calculation before confirming the answer. 
e.g. here I would say, "1% of 80 is 0.8. Since 0.5 is less than 0.8, it must be less than 1% of 80. So the answer has to be .625%"

ksp · Answer

Hey i go with VeritasPrepKarishma.

Perfect. I withdraw my answer choice.

Pedro13 · Answer

Karishma makes everything simple!

wontgiveup · Answer

Thanks all,finally I got it!

Karishma..as always your explinations are simple but awesome!!..Thanks a lot!!

GirijaChalapathy · Answer

Let the milk be =100litres +15%of water i.e 115 litres ...
0.8*100=80 ...be the C.P
115*0.7=80.5
Profit=0.5
%p=0.5*100/80=0.625

Posted from my mobile device

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quants profit and loss

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