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1. 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)

A. 8

B. 4

C. 16

D. 12

Solution:

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{aligned} \Rightarrow 9 a + 90 = 7 b + 70 \\ \Rightarrow 7 b - 9 a = 20...... (i) \\ Also, \frac{a - 2}{b - 2} = \frac{1}{3} \end{aligned}

By cross multiplying we get

\begin{aligned} \Rightarrow 3 a - 6 = b - 2 \\ \Rightarrow 3 a - b = 4..... (i i) \end{aligned}

Multiplying equation (ii) by 3

9 a - 3 b = 12..... (i i i)

Adding equation (ii) and (iii) we get

\begin{aligned} - 9 a + 7 b = 20 \\ 4 b = 32 \\ b = 8 year \end{aligned}

From equation (ii) we get

\begin{aligned} a = \frac{4 + b}{3} \\ = \frac{4 + 8}{3} \\ = \frac{12}{3} \\ = 4 year \end{aligned}

Since, Abhay is 4 years older to Niti
So, Abhay's present age = 8 + 4 = 12 years

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