A bucket contains 10L mixture of milk and water . First , 1L of mixture is removed and replaced by 1L of water. Then, 2L of mixture is removed and replaced by 2L of water. Finally , 3L of mixture is removed and replaced by 3L of water. If after all this milk and water becomes equal in the bucket. Then , how much liters of milk and water were there in the bucket at the starting ?
Answers
Answer:
Milk at starting was 8 litres and water was 2 litres
Explanation:
This is a bit confusing and complex Question so its answer will also be a bit difficult so stay focused, ok!!!
Let the amount of milk in litres be x and amount of water in litres be y
Now, we can split the question into 4 cases
Case 1
According to the Question,
x + y = 10 ----- 1
Case 2
According to the Question,
From eq.1
(x - (1/2)) + (y - (1/2) + 1) = 10 - 1 + 1
(x - (1/2)) + (y - (1/2) + (2/2)) = 10
(x - (1/2)) + (y + (1/2)) = 10 ----- 2
NOTE:- When we take 1 litre of the mixture, since water and milk is mixed together thoroughly, we can say that 1/2 litre of water and 1/2 litre of milk is taken (Think about it.....)
But for water 1 litre is added so 1 will be added
Also, do not open the bracket because, if we did open it, we would come back to x + y = 10
Case 3
According to the Question,
From eq.2, similarly
(x - (1/2) - 1) + (y + (1/2) - 1 + 2) = 10 - 2 + 2
(x - (1/2) - (2/2)) + (y + (1/2) + 1) = 10
(x - (3/2)) + (y + (1/2) + (2/2)) = 10
(x - (3/2)) + (y + (3/2)) = 10 ----- 3
Case 4
According to the Question,
From eq.3, similarly
(x - (3/2) - (3/2)) + (y + (3/2) - (3/2) + 3) = 10 - 3 + 3
(x - (6/2)) + (y + 3) = 10
(x - 3) + (y + 3) = 10 ------ 4
Now, we know that at this point amount of milk is equal to the amount of water
So,
x = y
Putting x = y in eq.1, we get
y + y = 10
2y = 10
y = 5
so, x = 5
Now, if this is true then (from eq.4)
(x - 3) = 5
then, x = 8
Similarly, (y + 3) = 5
y = 2
(I used the word "If" because in the Question they have said that "if they are equal.")
We can also check this, it will be true
See, at the end added water is (1 + 2 + 3) = 6 litres
but from water itself (1/2),1 and (3/2) is taken away as part of mixture
so, total added water will be
(6 - (1/2) - 1 - (3/2)) = 3 litres
we proved that at the end water will be equal to milk and will be 5 litres
But we came to know that 3 litres of water was added to water to get 5 litres so,
y + 3 = 5
y = 5 - 3
y = 2 litres
then, x = 8 litres (because x + y = 10)
(This is another way of solving this Question, this method is only for understanding and can't be used in exams, must use the above 4 cases method)
If you didn't understand this typing I have put up an image of my written derivation
So, amount of milk in the bucket at starting was 8 litres and amount of water at starting was 2 litres
Hope it helped and you understood it........All the best
