Question

Shubham’s age today is 12 years and his father is 42 years. Shubham’s mother is younger than his father by 6 years. Find the following ratios.
1. Ratio of Shubham’s age today to his mother’s age today.
2. Ratio of Shubham’s mother's age today to his father’s age today.
3. The ratio of Shubham’s age to his mother’s age when Shubham was 10 years old.

Answer 1

Hint: Here, we first find the age of Shubham’s mother and then we can easily find the required ratios.
Also to find the Shubham’s mother's age when he was 10 years old we can simply find her age 2 years back by subtracting 2 from her present age.

Complete step-by-step answer:
Since, it is given that Shubham’s mother's age is 6 years less than the age of his father. So, we can find the age of Shubham’s mother by subtracting 6 years from the age of his father.

Also, it is given that the age of Shubham’s father is 42 years. So, the age of Shubham’s mother will be:
= 42-6 = 36 years

Now, we have to find the ratios.

So, for the 1st case i.e. :
Ratio of Shubham’s age today to his mother’s age today= $\dfrac{Shubham's\,age\,today}{His\,mother's\,age\,today}$
                                                                                                    = $\dfrac{12}{36}$

On dividing numerator and denominator here by 12, we get:
Ratio of Shubham’s age today to his mother’s age today = $\dfrac{1}{3}$

Now, in the same way we can find the ratio of the 2nd case.

Since, we know that Shubham’s mother's age today is 36 years and his father’s age is 42 years.

So, the ratio of his mother’s age today to his father’s age today is= $\dfrac{His\,\,mother's\,\,age\,\,today}{His\,\,father's\,\,age\,\,today}$
                                                                                                                      = $\dfrac{36}{42}$

Now, to simplify this ratio on dividing the numerator and denominator by 6, we get:
The ratio of his mother’s age today to his father’s age today= $\dfrac{6}{7}$
Now, for the 3rd case:

Since we know that today when Shubham’s age is 12 years his mother’s age is 36 years , so when Shubham is 10 years old i.e. two years back her mother’s age will be:
= 36-2=34 years

So, the ratio of Shubham’s age to his mother's age when he was 10 years old i.e. 2 years back is =$\dfrac{Shubham's\,\,age\,\,two\,years\,\,back}{His\,\,mother's\,\,\,age\,\,two\,years\,\,back}$
= $\dfrac{10}{34}$

On dividing numerator and denominator by 2 we get:
The ratio of Shubham’s age to his mother's age when he was 10 years old i.e. 2 years back is = $\dfrac{5}{17}$

Note: Here it should be kept in mind that when we have to find the ratio some quantity ‘a’ to another quantity ‘b’, we have to divide a by b and not b by a .