Question

Do the ratios $15cm$to $3m$ and $15seconds$ to $3minutes$ form a proportion ? Justify your answer.

Answer 1

Step 1 : Making the units same.

Given, $15cm:3m$ and $15seconds:3minutes$

Since $1m=100cm$,

$\begin{array}{rcl}\therefore 3m& =& 3\times 100cm\\ & =& 300cm\end{array}$

Now, the ratio is $=\frac{15}{300}=\frac{1}{20}$

$=1:20$

Similarly,

Since, $1min.=60sec$

$\begin{array}{rcl}\therefore 3min.& =& 3\times 60sec\\ & =& 180sec\end{array}$

Now, the ratio is $=\frac{15}{180}=\frac{1}{12}$

$=1:12$

Step 2 : Verifying whether the given ratios are in proportion or not.

As, now we have both the ratios i.e.,$1:20$and $1:12$

And according to the proportion, the ratios should be equal.

But as we can see both the ratios are different from each other.

Hence, given ratios are not in proportion.