Question

Ratio of 10 hours to 300 minutes is
(A) \[\dfrac{3600}{600}\]
(B) \[\dfrac{1}{6}\]
(C) \[\dfrac{2}{1}\]
(D) \[\dfrac{5}{1}\]

Answer 1

Hint: For the calculation of ratio of 10 hours and 300 minutes, we have \[\dfrac{10\,hrs}{300\,\min }\] . The numerator and denominator have different units of time. So, first convert the unit of numerator into minutes by using the relation between hours and minutes, \[1hr=60\min \] . Now, solve it further and calculate the ratio.

Complete step-by-step solution:
According to the question, we are asked to find the ratio of 10 hrs and 300 minutes, that is,
The ratio of 10 hours and 300 minutes = \[\dfrac{10\,hrs}{300\,\min }\]
We can see that the above ratio has a different unit of time in numerator and denominator. So, we need to make the same unit of time in numerator as well as denominator.
First of all, we need to simplify 10 hrs. That is we need to convert 10 hours in minutes.
We know the relation between hours and minutes, \[1hr=60\min \] …………………………………..(1)
Let us convert 10 hours in minutes by using the relation between hours and minutes as shown in equation (1).
On multiplying by 10 in LHS and RHS of equation (1), we get
\[\Rightarrow 1hr\times 10=60\min \times 10\]
\[\Rightarrow 10hrs= 600\min \] …………………………………………(2)
For ratio of 10 hours and 300 minutes, we have
\[=\dfrac{10\,hrs}{300\,\min }\] ………………………………………………………(3)
Now, using equation (2) and on substituting 10 hrs by 300 min in equation (3), we get
\[=\dfrac{600\,\min }{300\,\min }\]
We can again simplify it as
\[= 2 \] ………………………………………….(4)
From equation (4), we have the ratio of 10 hrs and 300 minutes.
Now, observing the options provided, we can see that both option (A) \[\dfrac{600}{300}\] and option (C) \[{2}\] are correct.

Note: For this type of question, always try to approach by using the relation between hours and minutes that is, \[1hr=60\min \] . This will make our solution easy to solve within limited time constraints.