Question

Find the ratio of the following.
(i)Speed of a cycle 15km per hour to the speed of a scooter 30 km per hour.
(ii) 5 m to 10 km
(iv)50 paise to Rs. 5

Answer 1

Hint: In this question we have to compare one value to another value respectively taking care of the units that must be the same. As in (i) and (ii) part the units are the same but in (iii) part you have to convert either in rupees or in paise.
Formula Used:
 \[1Rs = 100paise\] or \[1paise = \dfrac{1}{{100}}Rs\], \[1Km = 1000m\]

Complete step-by-step answer:
So, let us begin with the question:
(i)Speed of a cycle 15km per hour to the speed of a scooter 30 km per hour.
We are given: speed of cycle = 15km per hour and speed of scooter 30 km per hour.
\[Ratio = \dfrac{{speed{\rm{ }}of{\rm{ }}cycle}}{{speed{\rm{ }}of{\rm{ scooter}}}}\]
\[ \Rightarrow \dfrac{{15}}{{30}}\]
Now, let’s divide numerator and denominator with 15.
After dividing we get,
\[ \Rightarrow \dfrac{1}{2}\]
Now, 1 is not divisible by 2. Means we have got our ratio that is \[1:2\] .

(ii)5 m to 10 km
Firstly, convert 10m to m:
As, \[1Km = 1000m\]
We will multiply \[10Km = 10 * 1000m\]
\[ \Rightarrow 10000m\]
\[Ratio = \dfrac{5}{{10000}}\]
Now, let’s divide numerator and denominator with 5.
After dividing we get,
\[ \Rightarrow \dfrac{1}{{2000}}\]
Now, 1 is not divisible by 2000. Means we have got our ratio that is \[1:2000\] .
\[Ratio = 1:2000\]

(iii)50 Paise to Rs. 5
Firstly convert 5 Rs to paise:
As , \[1Rs = 100\,Paise\]
We will multiply 5Rs with 100 \[\therefore 5Rs = 5 * 100paise\]
Now both 50 paise and 5 rs are in the form of paise. So, we can now calculate the ratio.
$\Rightarrow$ \[Ratio = \dfrac{{50Paise}}{{500Paise}}\]
Cutting zeros from numerator and denominator.
$\Rightarrow$ \[Ratio = \dfrac{5}{{50}}\]
Now let’s divide 5 from numerator and denominator.
$\Rightarrow$ \[Ratio = \dfrac{1}{{10}}\]
Now, 1 is not divisible by 10. Means we have got our ratio that is \[1:10\].
$\Rightarrow$ \[Ratio = 1:10\]

Note: Divide the appropriate number from the numerator and the denominator as many times as we can until the numerator is not divisible by the denominator. Then rewrite the fraction as ratio.