Question

A bowl is half full of water. Four cups of water are then added to the bowl, filling the bowl to \[70\% \] of its capacity. How many cups of water are now in the bowl?
A.12
B.20
C.15
D.14

Answer 1

Hint:Here it is given that a half filled jug is almost \[70\% \] full after adding four cups of water to it, we have to find the amount of water present in the bowl in terms of the number of cups. We will find the total capacity of the bowl using the given percentage. From the total capacity we will find \[70\% \] to get the total number of cups.

Complete step-by-step answer:
If the bowl was already half full of water, then it was originally \[50\% \] full. Adding 4 cups of water increased the percentage by \[20\% \] of the total capacity of the bowl.
You can use the percent change formula to solve the total capacity of the bowl:
Let x is the number of caps
Percent Change =Original Value Change in Value​
\[ \Rightarrow \dfrac{{20}}{{100}} = \dfrac{4}{x}\]
Solve the equation, we get
\[ \Rightarrow \dfrac{1}{5} = \dfrac{4}{x}\]
\[ \Rightarrow x = 20\]
The total capacity of the bowl is 20 cups, but the question asks for the total number of cups currently in the bowl.
Again,
It is given that the bowl is \[70\% \] full.
We have to find the \[70\% \] of \[20\]
\[ \Rightarrow x = \dfrac{{70}}{{100}} \times 20\]
\[ \Rightarrow x = 14\]

Hence, there are 14 cups of water in the bowl.

So, the correct answer is “Option D”.

Note:After finding the total capacity of the bowl in terms of cups we will find the total number of cups by multiplying the capacity with\[70\% \]. It is due to the fact that from the total number of cups we will need only \[70\% \] of cups to fill \[70\% \] of water in the bowl.