Question

Linda filled a jug with water up to ${\frac{4}{5}}^{th}$ of its maximum capacity for the birds in the summer. When six cups of water were taken out and four cups of water were poured into it, it was ${\frac{3}{4}}^{th}$ full. How many cups of water is required to fill the empty jug completely?

• A. 50 cups
• B. 40 cups
• C. 45 cups
• D. 35 cups

Answer 1

The correct option is B 40 cups

Let the capacity of the jug = $\text{V}$
The capacity of the cup = $\text{C}$
The jug was initially ${\frac{4}{5}}^{th}$ full.

Six cups of water were taken out and four cups of water were poured into it.
So, the volume became ${\frac{3}{4}}^{th}$ of the total.


Intitial volume – Cups taken out + Cups poured = Final volume

Let, the capacity of each cup be 'N'

$\Rightarrow \frac{4\text{V}}{5}-6\text{N}+4\text{N}=\frac{3\text{V}}{4}$

$\frac{4\text{V}}{5}-2\text{N}=\frac{3\text{V}}{4}$

$\frac{4\text{V}}{5}-\frac{3\text{V}}{4}=2\text{N}$

$\frac{16\text{V}-15\text{V}}{20}=2\text{N}$

$\frac{\text{V}}{20}=2\text{N}$

$\text{V}=20\times 2\text{N}$
$\text{V}=40\text{N}$

A total of 40 cups of water are required to fill the jug completely.