Do the ratios 15 cm to 2 m and 10 sec to 3 minutes form a
proportion?

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Solution

We know that, Two quantities in a ratio must be in the same units.

$1 m = 100 c m \Rightarrow 2 m = 200 c m$
$Ratio of 15 c m : 2 m = 15 c m : 200 c m = \frac{15 c m}{200 c m} = 3 : 40$

$Now, 1 m i n = 60 s e c \Rightarrow 3 m i n = 180 s e c$
$Ratio of 10 s e c : 3 m i n = 10 s e c : 180 s e c = \frac{10 s e c}{180 s e c} = 1 : 18$

For proportion both ratios must be equal, but $3 : 4 \neq 1 : 18.$
Hence, they are not in proportion.

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