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

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## 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 $$1:10$$

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