# Ex.8.1 Q1 Comparing Quantities - NCERT Maths Class 8

## Question

Find the ratio of the following.

(i) Speed of a cycle \(15\,\rm{ km}\) per hour to the speed of scooter \(30\,\rm{ km}\) per hour.

(ii) \(5\,\rm{ m}\) to \(10\,\rm{ km}\)

(iii) \(50\) paise to \(\rm{Rs}\, 5\)

## Text Solution

**What is known?**

Value of two quantities, which needs to be compared.

**What is unknown?**

Ratio

**Reasoning:**

A relationship between two quantities is normally expressed as the quantity of one divided by the other.

**Steps:**

**(i):**

Speed of a cycle \(= 15 \;\rm{km/hr}\)

Speed of a scooter \(= 30\,\rm{ km/hr}\)

Speed of cycle: Speed of scooter \(\begin{align}=\frac{{{15}}}{{{30}}}=\frac{{1}}{{2}} \end{align}\)

The answer is \(1:2\)

**(ii)**

Given data: \(5\,\rm{ m}\) to \(10 \,\rm{km}\)

Quantities can be compared only when the units are same.

\(1 \rm{km} = 1000 \rm{m}\)

Therefore, \(10\,\rm{ km} = 10 \times 1000 = 10000\,\rm{ m}\)

\(5\, \rm{m}\) to \(10\,\rm{ km}\) \(= 5\,\rm{m}\) to \(10000 \,\rm{m}\) \(\begin{align}=\frac{{5}}{{{10000}}}{ = }\frac{{1}}{{{2000}}}\end{align}\)

The answer is \(1:2000 \)

**(iii)**

Given data: \(50\) paise to \(\rm{Rs}\, 5\)

Quantities can be compared only when the units are same.

\[\begin{align}\rm{Rs}\, 1 &= 100\,\text{ paise}\\\rm{Rs} \,5 &= 5 \times 100\,\text{paise}\\ &= 500\, \text{paise}\end{align}\]

\(50\) paise to \(\rm{Rs}\, 5 = 50\) paise to \(500\) paise

\[\begin{align}\frac{{50}}{{500}} = \frac{1}{{10}} \end{align}\]

The answer is \(1:10\)