Question

Is the following statement true?
45 km : 60 km = 12 hours : 15 hours.
(A) True
(B) False

Answer 1

Hint: Convert both the ratios into their most reducible form by cancelling out the common factors from both the terms in each ratio. And then compare both the ratios for if they are equal or not.

Complete step by step answer:
According to the question, the first ratio is 45 km : 60 km. This can be simplified as:
$ \Rightarrow \dfrac{{45{\text{ km}}}}{{60{\text{ km}}}} = \dfrac{{3 \times 15}}{{4 \times 15}} = \dfrac{3}{4} .....(i)$
And the second ratio is 12 hours: 15 hours. This can also be simplified as:
$ \Rightarrow \dfrac{{12{\text{ hours}}}}{{15{\text{ hours}}}} = \dfrac{{4 \times 3}}{{5 \times 3}} = \dfrac{4}{5} .....(ii)$
Now, comparing ratios in equations $(i)$ and $(ii)$, we can say that they are not equal. So we have:
$ \Rightarrow $ 45 km : 60 km $ \ne $ 12 hours : 15 hours.
Hence the given statement is false.

So, (B) is the correct option.

Note: The first ratio is the ratio of two distances and the second ratio is the ratio of two time durations. In ratio, quantities with the same units are usually compared.