Question

Six year ago, the ratio of the ages of Kunal and Sagar was 6:5. Four years hence, the ratio of their ages will be 11:10. What is Sagar’s age at present?
 A. 16 years
 B. 18 years
 C. 20 years
 D. Cannot be determined
 E. None of these

Answer 1

Hint: First let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively. Then calculate their present ages. So, their present ages are 6x + 6 and 5x + 6. And also, their age after 4 years will be (6x + 6 + 4) and (5x + 6 + 4) respectively in this question. After this form the equation and solve it to get an answer.

Complete step-by-step answer:
In the question, the ratio of ages of Kunal and Sager before six year ago = 6:5.
So first let the age of Kunal six year ago be 6x.
And the age of Sagar six year ago was 5x.

According to question:
Four years hence, the ratio of their ages will be 11:10.
Age after 4 years,
Kunal’s age = 6x + 10
Sagar’s age = 5x + 10
Now,
$ \Rightarrow $$\dfrac{{{\text{11}}}}{{{\text{10}}}}{\text{ = }}\dfrac{{{\text{6x + 10}}}}{{{\text{5x + 10}}}}$
$ \Rightarrow $${\text{11(5x + 10) = 10(6x + 10)}}$
$ \Rightarrow $55x + 110 = 60x + 100
$ \Rightarrow $5x = 10
$ \Rightarrow $ x =2
Now, Age after 4 years,
Kunal’s age = 6x + 10
                   = 6$ \times $2 + 10
                   = 22 years
Sagar’s age = 5x + 10
                  = 5$ \times $2 + 10
                  = 20 years
Therefore, we can write:
Kunal ‘s present age = 6x + 6
                                 = 6$ \times $2 + 6
                                 = 18 years
Sagar’s present age = 5x + 6
                                 = 5$ \times $2 + 6
                                 = 16 years
So, option A is correct.

Note: Equation is a convenient way to represent conditions or relations between two or more quantities. For example, if the age of a person is ‘x’, then ‘n’ years after today, the age = x + n. similarly, n years in the past, the age of this would have been x – n years.