Question

Sleeping time of a python in a 24-hour clock is represented by the shaded portion in the figure. The ratio of sleeping time to awake time is ______.

Answer 1

Hint: In the figure, the circle is divided into four quarters, out of which three are shaded. Since each quarter represents six hours, sleeping hours is three times six and awake time is one time six. Using this we can calculate the ratio.

Useful formula:
The ratio of a quantity $x$ to a quantity $y$ is equal to $\dfrac{x}{y}$, which is also written as $x:y$.

Complete step by step solution:
In the figure, the shaded portion represents the sleeping time of python and the unshaded portion represents the awake time of python.
Let the sleeping time and awake time of python be ${T_S}$ and ${T_A}$ respectively.
Since the circle is divided into four quarters out of which three is shaded and each quarter contains six hours,
Sleeping time of python is three times six, which is equal to $18$ hours.
$ \Rightarrow {T_S} = 18hours$
Awake time of python is the unshaded portion, which contains one quarter of the circle.
So awake time $6 \times 1 = 6$ hours.
$ \Rightarrow {T_A} = 6hours$
We are asked to find the ratio of sleeping time to awake time.
The ratio of a quantity $x$ to a quantity $y$ is equal to $\dfrac{x}{y}$ which is also written as $x:y$.

Therefore, the required ratio is $\dfrac{{{T_S}}}{{{T_A}}} = \dfrac{{18}}{6} = \dfrac{3}{1}$
Ratio of sleeping hours to awake hours is $3:1$.

Note: Order is important when taking ratios. The ratio of a quantity $x$ to a quantity $y$ is equal to $\dfrac{x}{y}$. At the same time, the ratio of quantity $y$ to quantity $x$ is equal to $\dfrac{y}{x}$ .