Question

Do the ratio $15$ cm to $12$ m and $10$ sec to $3$ minutes form a proportion?

Answer 1

Step 1 : Conversion of quantity in same unit
In a portion,the first two terms(quantities) must be the same kind and of the same unit, whereas the last two terms (quantities) must also be of the same kind and the same unit.
Since, $1$m=$100$ cm and $1$ min = $60$sec
Now, $2$ m =$2\times 100$cm
=$200$ cm and
$3$ min=$3\times 60sec$
=$180sec$
Step 2: Check whether the ratio formed is in the portion or not
Given, $15cm:2m$=$10sec:3min$
Then,the ratio becomes,
$\Rightarrow 15:200$ = $10:180$
(From step 1)
$\Rightarrow 15:200$ =$\frac{15}{200}$=$\frac{5\times 3}{5\times 40}$=$\frac{3}{40}$ and
$10:180$ =$\frac{10}{180}$=$\frac{10\times 1}{10\times 18}$=$\frac{1}{18}$
$\therefore$ Ratio $15:200\ne$ Ratio $10:180$
Hence, they do not form the proportion.