Question

What is the ratio of \[1\] m $50$ cm to $1$ m \[80\] cm ?
(a) None of these
(b) $5:7$
(c) $6:5$
(d) $5:6$

Answer 1

Hint: The given problem revolves around the concepts of ‘ratio and proportion’. Keeping in mind, convert the parameter in any one of the measurements (from cm to m), say in ‘m’ by dividing the value in ‘cm’ by 100. As a result, to find the respective ratio, dividing both the given parameters (or, value) simultaneously in simplest form, to get the desired ratio.

Complete step-by-step solution:
Since, we have given that,
\[1\] m $50$ cm
On the other hand,
$1$ m \[80\] cm
Converting the above given values say, measurement in ‘m’ to ‘cm‘ or in ‘cm‘ to ‘m‘, we get
Here, we will convert ‘cm‘ to ‘m‘ , by the standard measurement that is $100$ cm $ = $ $1$ m, we get
\[1\] m $50$ cm $ = $ $1$ m $\dfrac{{50 \times 1}}{{100}}$ m
Hence, (by solving mathematically) the equation becomes
\[1\] m $50$ cm $ = $ $1$ m $\dfrac{1}{2}$ m
Also, can be written as (by adding the values)
\[1\] m $50$ cm $ = $ $1 + 0.5$ m
\[1\] m $50$ cm $ = $ $1.5$ m … ( i )
Similarly,
For the other value that is $1$ m \[80\] cm, we get
\[1\] m $80$ cm $ = $ $1$ m $\dfrac{{80 \times 1}}{{100}}$ m
Hence, (by solving mathematically) the equation becomes
\[1\] m $80$ cm $ = $ $1$ m $\dfrac{4}{5}$ m
Also, can be written as (by adding the values)
\[1\] m $80$ cm $ = $ $1 + 0.8$ m
\[1\] m $80$ cm $ = $ $1.8$ m … (ii)
Now, as a result the ratio of the given values is,
(Solving the ratios mathematically by dividing , simplifying , etc., we get)
 $\dfrac{{\;1m{\text{ }}50\;cm}}{{1m{\text{ }}80\;cm}}{\text{ = }}\dfrac{{1.5}}{{1.8}}$
Removing decimal by multiplying and dividing the equation by $10$, we get
$\dfrac{{\;1m{\text{ }}50\;cm}}{{1m{\text{ }}80\;cm}}{\text{ = }}\dfrac{{15}}{{18}}$
Multiplying and dividing by $3$, we get
$\dfrac{{\;1m{\text{ }}50\;cm}}{{1m{\text{ }}80\;cm}}{\text{ = }}\dfrac{5}{6}$
Also, represented as (in the form of ratio)
$1m{\text{ }}50\;cm{\text{ }}:{\text{ }}1m{\text{ }}80\;cm{\text{ = 5 }}:{\text{ }}6$
$\therefore \Rightarrow $The option (d) is correct.

Note: One must be able to know how to convert the standard measurements for the calculations such as $100$ cm $ = $ $1$ m, $1000$ km $ = $ $1$ m, etc. to find the ratio particularly. To calculate the ratio the given parameters should be in the same format. Remember the ratio is to be in simplest form i.e. either in real format (avoid to get in decimal), so as to be sure of our final answer.