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Five years ago, Adil was thrice as old as Bharat. Ten years later Adil shall be twice as old as Bharat. To know the present ages of Adil and Bharat :
(i) form the linear equations representing the above information.
(ii) show that the system of equations is consistent with unique solution.
(iii) find the present ages of Adil and Bharat.
(i) form the linear equations representing the above information.
(ii) show that the system of equations is consistent with unique solution.
(iii) find the present ages of Adil and Bharat.
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Sol. Let the present ages of Adil and Bharat be '$x$' years and '$y$' years respectively.
(i) According to the given statements
$(x - 5) = 3 \times (y – 5)$
$\Rightarrow x - 3y = -10$ --- (1) (1 Mark)
$(x + 10) = 2 \times (y + 10)$
$\Rightarrow x - 2y = 10$ --- (2) (1 Mark)
(ii) Here, $\frac{a_1}{a_2} = \frac{1}{1}$, $\frac{b_1}{b_2} = \frac{-3}{-2}$ or $\frac{3}{2}$
Since $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$ (1 Mark)
Therefore, system of equations is consistent with unique solution.
(iii) Solving equations (1) & (2), we get
$x = 50$ and $y = 20$ (1+1 Mark)
Therefore, the present ages of Adil and Bharat are $50$ years and $20$ years respectively.
(i) According to the given statements
$(x - 5) = 3 \times (y – 5)$
$\Rightarrow x - 3y = -10$ --- (1) (1 Mark)
$(x + 10) = 2 \times (y + 10)$
$\Rightarrow x - 2y = 10$ --- (2) (1 Mark)
(ii) Here, $\frac{a_1}{a_2} = \frac{1}{1}$, $\frac{b_1}{b_2} = \frac{-3}{-2}$ or $\frac{3}{2}$
Since $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$ (1 Mark)
Therefore, system of equations is consistent with unique solution.
(iii) Solving equations (1) & (2), we get
$x = 50$ and $y = 20$ (1+1 Mark)
Therefore, the present ages of Adil and Bharat are $50$ years and $20$ years respectively.