Question

In a mixture 60 liters, the ratio of milk and water is $2:1$. If this the ratio is to be $1:2$, then the quantity of water to be further added is
A.30
B.40
C.50
D.60

Answer 1

Hint: First of all, we will find the quantity of water and milk from the given quantity of mixture and the ratio i.e. for milk the ratio will be $\dfrac{2}{3}$ of 60 liters mixture. Similarly, for water it can be written as $\dfrac{1}{3}$ of 60 liters mixture. Then from that we will find the quantity of water to make the ratio $1:2$ and we will get our required answer.

Complete step-by-step answer:
Now, first of all in the question it is given that the total quantity of mixture is 60 liters and the ratio of milk to that of water is $2:1$, so, we can say that the total part of milk will be 2 out of that 3 parts and the rest of the part will be water.
So, the quantity of milk in 60 liters of mixture can be given by,
$\text{Quantity of milk=60}\times \left( \dfrac{2}{3} \right)=40\ liters$
So, the quantity of water will be $60-40=20\ liters$.
Now, we are asked to add water so that the ratio becomes $1:2$,
So, we can say that after adding x quantity of water the ratio should be equal to $1:2$, which can be written mathematically as,
New quantity of water is $\left( 20+x \right)\ liters$
Now taking ratios, we will get,
$\dfrac{40}{20+x}=\dfrac{1}{2}$
On simplifying further, we will get,
$\Rightarrow 40\times 2=20+x$
$\Rightarrow x=80-20=60\ liters$
Hence, the new quantity of water will be 60 liters.
Thus, option (d) is correct.

Note: In such types of sums, students might make mistakes in taking ratios of the quantities. They might place $40+x$, in place of $20+x$ and take ratios of the quantities, but by doing so the sum will go wrong and we will not get the desired answer, so students should take care while taking ratios.