Question
Four times a certain two digit number is seven times the number obtained on interchanging its digits. If the difference between the digits is $4;$ find the number.
✓
Answer
Let $x$ be the number at the ten's place.
and $y$ be the number at the unit's place.
So, the number is $10x + y$.
Four times a certain two$-$digit number is seven times
the number obtained on interchanging its digits.
$\Rightarrow 4( 10x + y ) = 7( 10y + x )$
$\Rightarrow 40x + 4y = 70y + 7x$
$\Rightarrow 33x - 66y = 0$
$\Rightarrow x - 2y = 0 ....(1)$
If the difference between the digits is $4$, then
$\Rightarrow x - y = 4 ...(2)$
Subtracting equation $(1)$ from equation $(2),$ we get :
$x - y = 4$
$- x - 2y = 0$
$- + - $
$y = 4$
Subtracting $y = 4$ in equation $(1),$ We get
$x - 2(4) = 0$
$\Rightarrow x = 8$
$\therefore $ The number is $10x + y = 10(8) + 4 = 84.$
and $y$ be the number at the unit's place.
So, the number is $10x + y$.
Four times a certain two$-$digit number is seven times
the number obtained on interchanging its digits.
$\Rightarrow 4( 10x + y ) = 7( 10y + x )$
$\Rightarrow 40x + 4y = 70y + 7x$
$\Rightarrow 33x - 66y = 0$
$\Rightarrow x - 2y = 0 ....(1)$
If the difference between the digits is $4$, then
$\Rightarrow x - y = 4 ...(2)$
Subtracting equation $(1)$ from equation $(2),$ we get :
$x - y = 4$
$- x - 2y = 0$
$- + - $
$y = 4$
Subtracting $y = 4$ in equation $(1),$ We get
$x - 2(4) = 0$
$\Rightarrow x = 8$
$\therefore $ The number is $10x + y = 10(8) + 4 = 84.$
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