170
The sum of the digit at tens place and twice the digit at unit place of a $2$-digit number is $16$. The sum of the number and the number obtained by reversing the digits is $121$. Express the given information as a system of linear equations in two variables. Hence, find the original number.
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Let the digit at unit place be $x$ and at tens place be $y$
$\therefore 2x + y = 16$ ------ (1) (1/2 Mark)
Original Number $= 10y + x$ (1/2 Mark)
Reverse number $= 10x + y$ (1/2 Mark)
$10y + x + 10x + y = 121$
$11x + 11y = 121$ or $x + y = 11$ ------ (2) (1/2 Mark)
Solving (1) and (2), we get $x = 5$ and $y = 6$ (1 + 1/2 Mark)
The original number is $65$. (1/2 Mark)
$\therefore 2x + y = 16$ ------ (1) (1/2 Mark)
Original Number $= 10y + x$ (1/2 Mark)
Reverse number $= 10x + y$ (1/2 Mark)
$10y + x + 10x + y = 121$
$11x + 11y = 121$ or $x + y = 11$ ------ (2) (1/2 Mark)
Solving (1) and (2), we get $x = 5$ and $y = 6$ (1 + 1/2 Mark)
The original number is $65$. (1/2 Mark)