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.

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5 years 10 months

6 years 10 months

5 years 20 months

5 years 40 months

answer is A.

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Detailed Solution

Concept- The age difference between Amit and Archana is provided. First, we multiply the ratio by a common variable to get the number. The value of the variable can then be determined by equating this number with the supplied age.
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 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

4 x = 56 \Rightarrow x = 14

Now using this value we can calculate the age of Archana.
∴ Age of Archana =

5 x = 5 \times 14 = 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”.
Hence, option 1 is correct.

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