Question

A vessel contains 180 litres of mixture of milk and water in the respective ratio of 13 : 5. Fifty-four litres of this mixture was taken out and replaced with 6 litres of water, what is the approximate percentage of water in the resultant mixture?

Answer 1

Answer: There is 31.06% of water in the resultant mixture.

Step-by-step explanation:

Since we have given that

Amount of mixture of milk and water in a vessel = 180 liters

Ratio of milk and water is given by

$13:5$

So, Amount of milk in the mixture is given by

$\frac{13}{18}\times 180\\\\=13\times 10\\\\=130$

Amount of water in the mixture is given by

$\frac{5}{18}\times 180\\\\ =5\times 10\\\\=50\ liters$

According to question, 54 liters of this mixture was taken out.

Amount of milk is taken out is given by

$\frac{13}{18}\times 54\\\\=13\times 3\\\\=39\ liters$

Amount of water is taken out is given by

$\frac{5}{18}\times 54\\\\=5\times 3\\\\=15\ liters$

and replaced it with 6 liters of water.

So, it becomes,

$Milk=130-39=91\ liters\\\\And\\\\Water=50-15+6=41\ liters$

So, Approximate percentage of water in the resultant mixture is given by

$\frac{41}{91+41}\times 100\\\\=\frac{41}{132}\times 100\\\\=31.06\%$

Hence, there is 31.06% of water in the resultant mixture.