Ten years hence, the respective ratio between Simmi's age ans Niti's age will be 7 : 9. Two years ago, the respective ratio between Simmi's and Niti's age was 1 : 3. If Abhay is 4 years older then Niti, what is Abhay's present age ? (in years)

Answer: Option D

Let present ages of Simmi and Niti be a and b years respectively.
Ten years hence, the ratio between Simmi's age and Niti's age = 7 : 9
According to question
$$\frac{a+10}{b+10}=\frac{7}{9}$$
By cross multiplying we get
$$\begin{array}{rl}& \Rightarrow 9a+90=7b+70\\ & \Rightarrow 7b-9a=\mathrm{20......}(i)\\ & \text{Also},\frac{a-2}{b-2}=\frac{1}{3}\end{array}$$
By cross multiplying we get
$$\begin{array}{rl}& \Rightarrow 3a-6=b-2\\ & \Rightarrow 3a-b=\mathrm{4.....}(ii)\end{array}$$
Multiplying equation (ii) by 3
$$9a-3b=\mathrm{12.....}(iii)$$
Adding equation (ii) and (iii) we get
$$\begin{array}{rl}& -9a+7b=20\\ & 4b=32\\ & b=8\text{ year}\end{array}$$
From equation (ii) we get
$$\begin{array}{rl}& a=\frac{4+b}{3}\\ & =\frac{4+8}{3}\\ & =\frac{12}{3}\\ & =4\text{year}\end{array}$$
Since, Abhay is 4 years older to Niti
So, Abhay's present age = 8 + 4 = 12 years