Question

A tank can hold \[50\;{\rm{litres}}\]of water. At present, it is only 30% full. How many litres of water shall I put into the tank so that it becomes 50% full?

Answer 1

Hint: The above problem can be resolved using the concept and fundamentals of volume analysis of the given vessel. In the problem, it is given that the tank can hold 50 litres of water. At the start, only 30 % of the capacity is filled. So, we need to find the exact volume of water that is required to complete that 30 % upto 50 %. For this, we just need to apply the basic mathematical tools in the case to find the volumes respectively. Then the final result is obtained by taking the difference of the capacities.

Complete step by step answer:
Given:
The capacity of the tank is, \[V = 50\;{\rm{litres}}\].
As, it is given in the problem that 30 % of the capacity is 50 % of the capacity.
Then frame the above statement in terms of numerical equation as,
\[\begin{array}{l}
{V_1} = 30\% \;of\;capacity\\
\Rightarrow {V_1} = \dfrac{{30}}{{100}} \times 50\;{\rm{litres}}\\
\Rightarrow {V_1} = 15\;{\rm{litres}}
\end{array}\]
Further obtain the value as,
\[\begin{array}{l}
{V_2} = 50\% \;of\;capacity\\
\Rightarrow {V_2} = \dfrac{{50}}{{100}} \times 50\;{\rm{litres}}\\
\Rightarrow {V_2} = 25\;{\rm{litres}}
\end{array}\]
The volume required to reach the 50 % full capacity as,
\[V = {V_2} - {V_1}\]
Substitute the value as,
 \[\begin{array}{l}
V = {V_2} - {V_1}\\
\Rightarrow V = 25\;{\rm{litres}} - 15\;{\rm{litres}}\\
\Rightarrow V = 10\;{\rm{litres}}
\end{array}\]
 Therefore, 10 litres of water should be filled into the tank so that it becomes 50% full.

Note:
Try to understand the concepts under the volume analysis, along with the basic mathematical operations involved in the analysis of the situation. It is also important to remember the fundamentals involved in the situation analysis, as this can help determine or frame various mathematical as well as the logical expressions.