Question

Find the ratio of 35min to 45seconds in simplest form.
A) 35:45
B) 7:9
C) 2100:45
D) 140:3

Answer 1

Hint:
In this ratio to the simplest form problem first we will convert the quantity in any one unit either in minutes or in seconds. We will see both the cases.

Complete step by step solution:
Case1: ratio of minutes
We know that 1min= 60seconds
So 45seconds= \[\dfrac{{45}}{{60}}\text{minutes}\]
Then, ratio of minutes will be
\[
   \Rightarrow \dfrac{{35}}{{\dfrac{{45}}{{60}}}} \\
   \Rightarrow \dfrac{{35 \times 60}}{{45}} \\
   \Rightarrow \dfrac{{35 \times 4}}{3} \\
   \Rightarrow \dfrac{{140}}{3} \\
 \]
Thus \[\dfrac{{140}}{3}\] is the simplest form. Now let’s check the second case.
Case2: ratio of seconds
We know that 1min= 60seconds
So 35minutes= \[35 \times 60 \text{seconds}\]
Then, ratio of seconds will be
\[
   \Rightarrow \dfrac{{35 \times 60}}{{45}} \\
   \Rightarrow \dfrac{{35 \times 4}}{3} \\
   \Rightarrow \dfrac{{140}}{3} \\
 \]
Thus \[\dfrac{{140}}{3}\] is the simplest ratio of seconds.
So we conclude that \[\dfrac{{140}}{3}\] is the simplest ratio.

So option D is correct.

Note:
Here look at the options carefully. Option A is given the ratio directly and it is not in simplest form and same unit. Option B is in simplest form but it is obtained from suppose option A and hence not in the same unit. So both options are wrong.
But option D is in same unit say \[ \Rightarrow \dfrac{{35 \times 60}}{{45}} \Rightarrow \dfrac{{2100}}{{45}} \Rightarrow \dfrac{{140}}{6}\] but not in simplest form.
So students definitely check other or similar meaning options also but tick the correct only.