Question

What is the ratio in between $7$ months and $7$ years?
(a) $1:12$
(b) $1:13$
(c) $1:14$
(d) None of these.

Answer 1

Hint: This question is based on the ratio and unitary method concept. In this question, we have to calculate the ratio between months and years. But, we know that the ratio is only calculated between two same units. So we have to get both in months or years using –
$1year=12months$.
By getting both in same units, we get ratio by using following formula:
If ${{r}_{1}}$ and ${{r}_{2}}$ are in same units,
${{r}_{1}}:{{r}_{2}}=\dfrac{{{r}_{1}}}{{{r}_{2}}}$.

Complete step by step answer:
Now, before getting started with the solution, let us learn about the concept. The unitary method is a method for solving a problem by first finding the value of a single unit and then finding the necessary value by multiplying the single unit value.
Now, we have to calculate the ratio between $7$ months and $7$ years, but we know that ratio is calculated only between the same units. So we have to change both into months.
As we know that there are $12$ months in one year, so by unitary method:
$\because 1year=12months$
$\therefore 7year=7\times 12months$
$=84months.$

Let us assume ${{r}_{1}}=7months$ and${{r}_{2}}=7years$.
So, we have
${{r}_{1}}:{{r}_{2}}=\dfrac{{{r}_{1}}}{{{r}_{2}}}$
$\Rightarrow 7months:7years=\dfrac{7months}{7years}$
$\because 7years=84months$
$\Rightarrow 7months:7years=\dfrac{7months}{84months}$
$=\dfrac{1}{12}$
So, we have got the ratio as ${{r}_{1}}:{{r}_{2}}=1:12$.

Hence, $7months:7years=1:12$, and the correct option is (a).

Note:
In this question, students should take care of units. First of all, we should convert both quantities into the same units. Many students directly divide quantities to each other without changing units, which is wrong. In this question, we can convert both quantities into year also.
As we know,$12months=1year$.
So, by unitary method:
$1month=\dfrac{1}{12}year$
$\Rightarrow 7month=\dfrac{7}{12}year$.
And then we can calculate ratio –
 $7months:7years=\dfrac{7months}{7years}$
\[\Rightarrow 7months:7years=\dfrac{\dfrac{7}{12}year}{7year}\]
$=\dfrac{1}{12}$
$=1:12$.