We have 100 litres of a mixture of milk and water which is 10% water. How much more pure milk should be added so that the new mixture has only 5% water (Answer - 4 litres).
#Mathematics
#RatioAndProportion
Answers
Total mixture of water and pure milk = 100 liter
Quantity of water in the mixture = 10 %
Quantity of water in liters = 10 liters
Quantity of pure milk in liters = 100 - 10 = 90 liters
Let 'x' liters of pure milk is added to the mixture to make water 5 % and Pure milk 95 %
Total amount of pure milk becomes (90 + x) liter and total amount of mixture becomes (100 + x) liters.
⇒ (90 + x) = (95/100)*(100 + x)
⇒ (90 + x) = (19/20)*(100 + x)
⇒ (90 + x)*20 = 19*(100 + x)
⇒ 1800 + 20x = 1900 + 19x
⇒ 20x - 19x = 1900 - 1800
⇒ x = 100 liter
So, 100 liters of pure milk should be added so that the new mixture (200 liters) has only 5 % water.
Let us check our answer :-
Old mixture = 100 liters
Quantity of water in old mixture = 10 liters
Quantity of pure milk in old mixture = 90 liters
Quantity of pure milk added to the old mixture = 100 liters
Total quantity of new mixture after adding 100 liters of pure milk = 100 + 100
= 200 liters
Now,
Quantity of water after adding 100 liters of pure milk to the old mixture should be 5 % and quantity of water in liters will not not be changed. It will be 10 liters only.
Quantity of water in the new mixture = 10 liters
Therefore, rest is the quantity of pure milk in the new mixture i.e. 200 - 10 = 190 liters
Percentage of water = (10*100)/200
= 5 %
So, the quantity of water in the new mixture will not be changing and it will be 5 % of the new mixture.
Hence proved.
Quantity of water in the mixture = 10 %
Quantity of water in liters = 10 liters
Quantity of pure milk in liters = 100 - 10 = 90 liters
Let 'x' liters of pure milk is added to the mixture to make water 5 % and Pure milk 95 %
Total amount of pure milk becomes (90 + x) liter and total amount of mixture becomes (100 + x) liters.
⇒ (90 + x) = (95/100)*(100 + x)
⇒ (90 + x) = (19/20)*(100 + x)
⇒ (90 + x)*20 = 19*(100 + x)
⇒ 1800 + 20x = 1900 + 19x
⇒ 20x - 19x = 1900 - 1800
⇒ x = 100 liter
So, 100 liters of pure milk should be added so that the new mixture (200 liters) has only 5 % water.
Let us check our answer :-
Old mixture = 100 liters
Quantity of water in old mixture = 10 liters
Quantity of pure milk in old mixture = 90 liters
Quantity of pure milk added to the old mixture = 100 liters
Total quantity of new mixture after adding 100 liters of pure milk = 100 + 100
= 200 liters
Now,
Quantity of water after adding 100 liters of pure milk to the old mixture should be 5 % and quantity of water in liters will not not be changed. It will be 10 liters only.
Quantity of water in the new mixture = 10 liters
Therefore, rest is the quantity of pure milk in the new mixture i.e. 200 - 10 = 190 liters
Percentage of water = (10*100)/200
= 5 %
So, the quantity of water in the new mixture will not be changing and it will be 5 % of the new mixture.
Hence proved.