Question

A small tank is $\dfrac{2}{5}$ full of water is then poured into a large empty tank which has a capacity that is twice that of the small tank. What fraction of a large tank is filled with water?

Answer 1

Hint: Focus on the point that the volume of water for both the vessels will be equal. Start by taking the volume of the small tank be x. As it is given that the volume of the large tank is twice of the small tank, i.e., 2x. The volume of water is $\dfrac{2}{5}$ of the small tank, i.e., $\dfrac{2}{5}x$ . So, find the fraction of the volume of water to the volume of the large tank to get the answer.

Complete step-by-step answer:
Let us start the solution to the above question by letting the volume of the small tank be x.
As it is given that the volume of the large tank is twice that of the small tank, so we can say that the volume of the larger tank is 2x.

Also, the volume of water is $\dfrac{2}{5}$ of the small tank, so, we can say that the volume of water present is $\dfrac{2}{5}x$ . Now when the water is poured in the larger tank the volume of water is not changed, so the volume of water in the large tank is still $\dfrac{2}{5}x$ and the capacity of the large tank is 2x.
$\text{Fraction of large tank filled}=\dfrac{\text{volume of water}}{\text{volume of large tank}}=\dfrac{\dfrac{2}{5}x}{2x}=\dfrac{1}{5}$
Therefore, the answer to the above question is $\dfrac{1}{5}$.

Note:The point where students generally make a mistake is as soon as they read the words ‘volume of water’ they think about 3-D mensuration, volume of cylinder and let the radius and height of the cylinder to be variables, which will eventually give the answer in the above question as well but would be much more complex and time consuming, so it is a prescribed thing that you always read the question properly and try to figure out the constraints, and if a specific shape is mentioned then go for mensuration.