Question

Find the ratio of the following:
(a) $30$ minutes to $1.5$hours
(b) $40cm$ to $1.5m$
(c) $55$ paisa to Rs.$1$
(d) $500ml$ to $2litres$

Answer 1

Hint: When we compare the relationship between two numbers dealing with a kind, then we use the ratio formula. It is denoted as a separation between the number with a colon (:). Sometimes a division sign is also used to express ratios.

Complete step by step answer:
(a) We need to find the ratio of $30$ minutes to $1.5$ hours.
So we need to convert hours into minutes.
As we know, $1hour = 60 \text{minutes}$
Therefore, $1.5hours = 1.5 \times 60 \text{minutes}$
By removing the decimal point we get,
\[1.5hours = \dfrac{{15}}{{10}} \times 60 \text{minutes}\]
On further solving we get,
\[ \Rightarrow 1.5hours = (15 \times 6) \text{minutes} = 90 \text{minutes}\].
So,
Ratio= $\dfrac{{30 \text{minutes}}}{{90 \text{minutes}}}$
$=\dfrac{{30}}{{90}}$
Now converting it into its standard form we get,
$=\dfrac{1}{3}$.

$\therefore $ The required ratio is $1:3$.

(b) we need to find the ratio of $40cm$ to $1.5m$.
So, we need to convert $m$ into $cm.$
As we know, $1m = 100cm$
$1.5m = 1.5 \times 100cm$
By removing the decimal point we get,
$1.5m = \dfrac{{15}}{{10}} \times 100cm$
Now on cancelling 0’s we get,
$1.5m = (15 \times 10)cm = 150cm$.
So,
Ratio= $\dfrac{{40cm}}{{150cm}}$
Ratio= $\dfrac{{40}}{{150}}$
On canceling 0’s we get,
Ratio= $\dfrac{4}{{15}}$

$\therefore $ The required ratio is $4:15$.

(c) we need to find a ratio of $55$ paisa to Rs$1$. So, we need to convert Rupees into paise.
As we know, $Rs1 = 100paise$
$Rs1 = 1 \times 100paise = 100paise$
So,
Ratio= $\dfrac{{55paise}}{{100paise}}$
Ratio= $\dfrac{{55}}{{100}}$
Now converting it into its simplest form by dividing it by 5 we get,
Ratio= $\dfrac{{11}}{{20}}$

$\therefore $ The required ratio is $11:20$.

(d) We need to find the ratio of $500ml$ to $2litres$
So, we need to convert liter into ml.
As we know, $1litres = 1000ml$
Therefore, $2litres = 2 \times 1000ml = 2000ml$
So,
Ratio= $\dfrac{{500ml}}{{2000ml}}$
By cancelling 0’s and converting it into its simplest form by dividing it by 5 we get,
Ratio= $\dfrac{5}{{20}} = \dfrac{1}{4}$

$\therefore $ The required ratio is $1:4$.

Note:
 In order to find the ratios in the above question one must know the following relationships:
(i) $1hour = 60 \text{minutes}$
(ii) $1m = 100cm$
(iii) $Rs1 = 100paise$
(iv) $1litres = 1000ml$
While finding the ratios we can change hours to minutes or minutes to hours and same with $m$ to $cm$, $Rs$ to $Paise$, $lt$ to $ml$. Logic is just changing the values into the same units.
For example, in the first part of the given question,
We need to find a ratio of $30$ minutes to $1.5$ hours.
It can be done like, converting 30 minutes to hours.
$\Rightarrow 30$ minutes$= 0.5$ hour
The required ratio will be
$\Rightarrow \dfrac{30min}{1.5hr}=\dfrac{0.5hr}{1.5hr}$
$=\dfrac{5}{15}$
$=\dfrac{1}{3}$
Therefore the required ratio will be 1:3