Question

Present ages 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: Let Sameer and Anand respectively present age are x and y. Condition 1 is $\dfrac{x}{y}=\dfrac{5}{4}$ and condition 2 is $\dfrac{x+3}{y+3}=\dfrac{11}{9}$. Putting the value of x in condition 2 and solving it we get the value of y.

Complete step-by-step answer:
Let x and y be the present age of Sameer and the present age of Anand respectively.
According to the first condition,
$\dfrac{y}{x}=\dfrac{4}{5}$
Taking the cross multiplication, we get
$5y=4x$
$4x-5y=0...........(1)$
Three year hence, their ages will be - Sameer age x + 3 and Anand age y + 3 and the ratio of their ages 11: 9 accordingly
$\dfrac{x+3}{y+3}=\dfrac{11}{9}$
Taking the cross multiplication, we get
$9x+27=11y+33$
$9x-11y=6.........(2)$
Multiplying equation (1) by 9 and multiplying equation (2) by 4, subtracting equation (1) from equation (2) we get
$\left( 36x-44y \right)-\left( 36x-45y \right)=24-0$
$36x-44y-36x+45y=24$
$y=24$
Hence, the present age of Anand is 24 years.

Note: Alternatively, the question is solved as follows
Let the present ages of Sameer and Anand be 5x years and 4x years respectively
According the given condition,
$\dfrac{5x+3}{4x+3}=\dfrac{11}{9}$
Taking the cross multiplication, we get
$9\left( 5x+3 \right)=11\left( 4x+3 \right)$
$45x+27=44x+33$
Rearranging the terms, we get
$45x-44x=33-27$
$x=6$
Therefore, Anand's present age = 4x = 24 years.