Haryana Police Constable Model Paper 5

Given∶
Age difference between Shaad and Noor is of 20 years.
Ratio of their ages before 4 years = 2 ∶ 1
Formula Used∶
If $\mathrm{a}:\mathrm{b}=\mathrm{c}:\mathrm{d}$
Then product of Extremes = Product of means
$\Rightarrow \mathrm{a}\times \mathrm{d}=\mathrm{b}\times \mathrm{c}$
Calculation∶
Let Shaad’s present age be ‘x’ years and Noor’sage be ‘y’ years.
So, $\mathrm{x}-\mathrm{y}=20$ ----(1)
4 years before,
Shaad’s age was $\left(\mathrm{x}-4\right)$ years
Noor’s age was $\left(\mathrm{y}-4\right)$ years
According to question,
$\left(\mathrm{x}-4\right):\left(\mathrm{y}-4\right)$ years = 2 ∶ 1
$\Rightarrow \mathrm{x}-4=2\mathrm{y}-8$
$\Rightarrow \mathrm{x}-2\mathrm{y}=-4$ ----(2)
Subtracting eq (1) from (2), we get,
$\mathrm{y}=24$
Put $\mathrm{y}=24$ in eq (1)
$\mathrm{x}-\mathrm{y}=20$
$\Rightarrow \mathrm{x}-24=20$
$\Rightarrow \mathrm{x}=24+20=44$
∴ Shaad’s present age is 44 years and Noor’s present age is 24 years.