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# Seven times a two-digit number is equal to four times the number obtained by reversing the digits. If the difference between the digits is 3. Find the number.

Given :

Seven times a two-digit number is equal to four times the number obtained by reversing the digits.

The difference between the digits is 3.

To do :

We have to find the given number.

Solution :

Let the two-digit number be $10x+y$.

$x - y = 3$ or $y-x=3$

$x=3+y$ or $x=y-3$....(i)

The number formed on reversing the digits is $10y+x$.

Therefore,

$7(10x+y) = 4(10y+x)$

$70x+7y=40y+4x$

$70x-4x+7y-40y=0$

$66x-33y=0$

$11(6x-3y) = 0$

$6x-3y = 0$

$3y=6x$

$y=2x$.......(ii)

Substituting equation (i) in equation (ii), we get,

$y =2(3+y) $ or $y=2(y-3)$

$y = 6+2y$ or $y=2y-6$

$2y-y = -6$ or $2y-y=6$

$y=-6$ or $y=6$

This implies,

$y=6$ (Since $y$ cannot be negative)

$x=y-3$

$x= 6-3$

$x=3$

The original number is $10(3)+6 = 30+6 = 36$.

The original number is 36.

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