Question

The ages of Amit and Archana are in the ratio \[4:5\]. If Amit is 4 years, 8 months old, find the age of Archana.

Answer 1

Hint: We have given the age ratio of Amit and Archana. Firstly we convert the ratio into the number by multiplying with a common variable. After that, we can equate this number with the given age and calculate the value of the variable. This variable helps in finding the age of Archana.

Complete step-by-step answer:
 We have given that Ratio of ages of Amit and Archana = $ 4:5 $
So let the age of Amit = $ 4x $ ………(i)
Age of Archana = $ 5x $ …………..(ii)
Here x is the common variable of the age of Amit and Archana.
We have to calculate the value of x.
We have given that the age of Amit = 4 years 8 months. We have to convert this into months only, this will simplify our calculation. we know that one year = 12 months. So, 4 years = 4× 12 = 48 months.
4 years 8 months = \[48 + 8 = 56\] months.
So, age of Amit = 56 months ……………..(iii)
Now equate (i) and (iii) we get
 $ 4x = 56 \Rightarrow x = 14 $
Now using this value we can calculate the age of Archana.
∴ Age of Archana = \[5x{\text{ }} = {\text{ }}5 \times {\text{ }}14{\text{ }} = {\text{ }}70\] months
To calculate the age in years, divide 70 by 12 we get 5 years 10 months.
Age of Archana = 5 years 10 months.
So, the correct answer is “5 years 10 months”.

Note: We use a linear equation in one variable to solve this problem. The linear equation in one variable is the equation which is in the form ax+b = 0. Where a, b are integers and x is a variable. This linear equation has only one solution.