Question

Present age of Sameer and Anand are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Anand's present age in years?

Answer 1

Hint: We have the ratio of the age of anand and Sameer given in the question. First let the present age of sameer and anand be x. In the three year hence means three year after the present age so we have to add 3 year in the present age of anand and Sameer.

Complete step-by-step answer:
Let the present age of Anand and sameer be
Sameer present age = 5x
Anand present age = 4x
Given in the question that three year hence, the ratio of there age is 11:9
Add the three in the present age of Sameer and anand
Sameer age after three year
\[5x + 3 = 11x\]
Anand age after three year
$4x + 3 = 9x$
As we have the ratio of age so,Now solve both the equation in the from of ratio
$\dfrac{{5x + 3}}{{4x + 3}} = \dfrac{{11}}{9}$
 Do Cross multiply in the above equation
$ \Rightarrow 9(5x + 3) = 11(4x + 3)$
Open the brackets and multiply
$ \Rightarrow 45x + 27 = 44x + 33$
Solve the variable and constant part separately
$ \Rightarrow 45x - 44x = 33 - 27$
Subtract the variable and the constant term
$\therefore x = 6$
The present age of anand is $4x$
$ = 4 \times 6$
Multiply the numbers
$ = 24$years

Hence the present age of anand is 24 years.

Note: We used the concept of linear equations in one variable. We use linear equations in one variable when there is only one unknown variable. We use linear equations in two variables when two unknowns are there.