The mixture of milk and water in a flask is in the ratio of 2: 3, if 30 l mixture is taken out from the flask and 4 l milk added, then the new ratio of milk and water becomes 4: 5. Find the initial quantity of mixture in flask.
Answers
Answer: 80 litres
Step-by-step explanation:
According to the given information:
Let the initial quantity of milk in the flask be “2x” and the initial quantity of water in the flask be “3x”.
So, the initial quantity of the mixture = 2x + 3x = 5x
Step 1:
30 litre of the mixture is taken out from the flask
∴ The quantity of milk remaining in the flask after 30 L of the mixture is removed = 2x - [30 * 2/5] = 2x – 12
And,
∴ The quantity of water remaining in the flask after 30 L of the mixture is removed = 3x - [30 * 3/5] = 3x – 18
Step 2:
Again, 4 litres of milk is added.
∴ The final quantity of milk in the flask after adding 4 litres of milk = 2x – 12 + 4 = 2x – 8
Step 3:
After removing 30 L from the mixture and adding 4 L of milk the new ratio becomes 4:5.
Therefore, we can write the equation as,
[2x – 8] / [3x – 18] = 4/5
⇒ 10x – 40 = 12x – 72
⇒ 12x – 10x = 72 – 40
⇒ 2x = 32
⇒ x = 16 litres
Thus,
The initial quantity of the mixture in the flask is,
= 5x
= 5 * 16
= 80 litres