Question

16. Ten years hence, the respective ratio between Simmi's age and Niti's age will be 7:9.
Two years ago, the respective ratio between Simmi's age and Niti's age was 1:3. If
Abhay is 4 years older to his sister Niti, what is Abhay's Present age ? (in years)
[MBA, 2016)
(a) 8
(b) 4
(c) 16
(d) 12
(C) 20​

Answer 1

Let the Present Ages of Simmi and Niti Be x and y

A/Q

$\frac{7}{9} = \frac{x + 10}{y + 10} \\ = > 7y + 70 = 9x + 90 \\ = > 9x - 7y = - 20 \\ = > 7y - 9x = 20 \: \: ...(i) \\ \frac{1}{3} = \frac{x - 10}{y - 10} \\ = > y - 10 = 3x - 30 \\ = > 3x - y = 20 \: \: ...(ii)$

Now,

$eq(i) \: \times 1 = - 9x + 7y = 20 \\ eq(ii) \: \times ( - 3) = - 9x + 3y = - 60 \\ \\ = > 7y - 3y = 80 \\ = > 4y = 80 \\ = > y = 20$

Hence

Age of Niti Is 20 yrs.

So, Age of Abhay= 24 yrs.