Question

In the figure, Tank A is completely filled with water and Tank B is empty. Some water is poured from Tank A into Tank B so that the height of the water level in the two tanks are the same. What is the height of the water level in each tank?

Answer 1

Hint: First of all, find the total volume of water by finding the volume of the tank A. Now after pouring water into tank B, consider the height of both the tanks as h and again find the volume of water in each tank by using \[L\times B\times H\]. Now, add these volumes and equate it to the initial volume of water in tank A and from this find the volume of H that is the height of the water in each tank.

Complete step-by-step answer:

In this question, we are given that Tank A is completely filled with water and Tank B is empty. Some water is poured from Tank A into Tank B so that the height of the water level in the two tanks are the same. We have to find the height of the water level in each tank.

In the above figure, we can see that tank A is completely filled with water and tank B is empty. So, let us find the volume of the water in tank A.
We are given that length of tank A (L) = 15 cm, breadth of tank A (B) = 15 cm and height of tank A (H) = 20 cm……(i)
We can see that tanks are in the same cuboid and volume of cuboid = \[L\times B\times H\]. By using this, we get,
The volume of tank A = \[L\times B\times H\]
By substituting the values of L, B, and H from equation (i), we get, the volume of tank A
\[{{V}_{t}}=15cm\times 15cm\times 20cm\]
\[{{V}_{t}}=4500c{{m}^{3}}.....\left( i \right)\]
So, we get the volume of tank A or the quantity of water in tank A as \[4500c{{m}^{3}}\].

Now, we know that some water is poured from tank A to tank B so that the height of the water levels in two tanks are the same. So, let the height of the water level in each tank is ‘h’ as shown in the above figure.
Let us now find the volume of water in each tank.
Now, we have the length of tank A = 15 cm, breadth of tank A = 15 cm, the height of water in tank A = h cm.
So, we get the volume of water in tank A,
\[{{V}_{a}}=L\times B\times H\]
\[{{V}_{a}}=15\times 15\times h\]
\[{{V}_{a}}=225hc{{m}^{3}}.....\left( ii \right)\]
Also, we have the length of tank B = 25 cm, breadth of tank B = 11 cm, height of water in tank B = h cm.
So, we get the value of water in tank B,
\[{{V}_{b}}=L\times B\times H\]
\[{{V}_{b}}=25\times 11\times h\]
\[{{V}_{b}}=275hc{{m}^{3}}.....\left( iii \right)\]
We know that the same water which was initially in tank A is now in both tank A and tank B. That means the volume of the water will remain the same. So, we get,
(Final Volume of water in tank A) + (Final Volume of water in tank B) = (Initial Volume of water in tank A)
\[{{V}_{a}}+{{V}_{b}}={{V}_{t}}\]
By substituting the values of \[{{V}_{t}},{{V}_{a}}\text{ and }{{V}_{b}}\] from equation (i), (ii) and (iii) respectively, we get,
225h + 275h = 4500
500h = 4500
By dividing 500 into both sides, we get,
\[h=\dfrac{4500}{500}\]
\[h=9cm\]
So, we get the height of water in each tank as 9 cm.

Note: In this question, many students make this mistake of considering the volume of two tanks the same which is wrong because we are given that the only height of the water is the same and also the length and breadth of both tanks are different. So, the volume can’t be the same. So, this must be taken care of. Also, note the value of the liquid remains constant even if we pour it into another container as it is the amount of the liquid which does not change by pouring it into different containers unlike the surface area, etc. which changes.