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# Quantity Aptitude Question

A mixture of 50 litres of milk and water contain 10% of water. How much water must be added to make water 20% in the given mixture?
Amol

Answered On : Oct 26th, 2011

10 ltr.

Mark Haynes

Answered On : Oct 26th, 2011

That's wrong, realize as you add water to the mixture, the volume of the mixture increases as well. Thus if you added 10 ltr of water to the 50 ltr mixture you would get a 60 ltr mixture. made of 45 ltr milk and 15 ltr water. That's 25% water in the mixture, not the 20% water being asked.

So, from the start:

m = Milk
w = Water
x = amount of water to add

For the mixture without any additional water:

w = 5 ltr
m = 45 ltr

Thus :

(45 + (5 + x)) - ((45 + (5 + x)) * 8/10) = (5 + x)
(50 + x) - ((50 + x) * 8/10) = (5 + x)
(50 + x) - (40 + (x * 8/10)) = (5 + x)
(50 + x) = (5 + x) + (40 + (x * 8/10))
50 + x = 45 + x + (x * 8/10)
50 = 45 + (x * 8/10)
5 = x * 8/10
5 * 10/8 = x
6.25 = x

The new mixture = 56.25 ltr
And 20% of 56.25 = 11.25 ltr = 5 (original amount) + 6.25 (amount of water added)

Thus, How much water must be added to make water 20% in the given mixture?

6.25 ltr water

1 User has rated as useful.

Sweta

Answered On : Nov 1st, 2011

what formula did u use here:(45 + (5 + x)) - ((45 + (5 + x)) * 8/10) = (5 + x)

Saboo Sravan

Answered On : Nov 3rd, 2011

View all answers by Saboo Sravan

(45 + (5 + x)) - ((45 + (5 + x)) * 8/10) = (5 + x) is nothing but subtracting 80% from the whole mixture after adding water and equating it to the amount of water after addition........ :)

lohitha

Answered On : Dec 8th, 2011

In the question they asked "to make water 20% in the given mixture" means we have to calculate the 20% of water in 50ltrs only, not for other mixture I think. The answer will be 10ltrs.

Mark Haynes

Answered On : Dec 8th, 2011

Lohitha,

No, that is wrong. The question is:

"A mixture of 50 litres of milk and water contain 10% of water."

So, to start the mixture is 50 litres, of which 10% is water.

"How much water MUST BE ADDED to make water 20% in the GIVEN MIXTURE?"

Youre taking the existing mixture and ADDING WATER to it to get a GIVEN MIXTURE which is 20% water.

The answer is: 6.25 ltr water

vinoth

Answered On : Dec 14th, 2011

The ans is 10 ltr.

Mark Haynes

Answered On : Dec 15th, 2011

vinoth,

We know that there is 5 litres of water and 45 litres in the mixture of 50 litres of milk and water to start because were told the mixture contains 10% of water. The question is aiming for how much water must be added to make water 20% in the given mixture? Now, if you add the 10 litres of water you answered, you get a mixture which is 60 litres, of which 45 litres is milk and 15 litres is water which is 25% water not 20%.

Praveen

Answered On : Jan 8th, 2012

Instead of using - "45 + (5 + x)) - ((45 + (5 + x)) * 8/10) = (5 + x) " use simpler form i.e., (50+x)*20/100=5+x. Here x is the amount of water that is needed to add to mixture. So above equation simply translated as => "x" litres of water is added to a 50 litres mixture. You are adding that x litres of water to the mixture to iincrease the water percentage to 20. Hence 20% of total amount of mixture (50+x) will be equal to (earlier 5 litres of water + x litres of addition)

Mark Haynes

Answered On : Jan 10th, 2012

Praveen,

Yes, that will work as well. I guess, part of the reason I expanded the equation so was to show fully how I was getting the result. The equation: "(50 + x) * 20 / 100 = 5 + x" is totally correct:

(50 + x) * 20 / 100 = 5 + x
(50 + x) * 2 / 10 = 5 + x
(2 * (50 + x)) / 10 = 5 + x
(100 + 2x) / 10 = 5 + x
10 + (2x / 10) = 5 + x
5 + (2x / 10) = x
50 + 2x = 10x
50 = 8x
6.25 = x

karthik

Answered On : Nov 5th, 2012

100li