Question

the sum of two digit number and the number obtaining by reversing the order of its digits is 165. If the digits differ by 3, find the number. ​

Answer 1

Step-by-step explanation:

Hey mate

Question :-

The sum of two digit number and the number obtaining by reversing the order of its digits is 165. If the digits differ by 3, find the number.

Answer :-

Number = 69 or, 96

Explanation :-

Let the digits at units and tens place of the given number be x and y respectively.

Then,

$number \: = 10y + x \: \: \: \: ............. \: (eq1)$

Number obtained by reversing the order of the digits

$= 10x + y$

According to given conditions, we have

$(10y + x) + (10x + y) = 165 \\ and \: \: x - y = 3 \: or \: y - x = 3 \\ = > 11x + 11y = 165 \\ and \: x - y = 3 \: or \: y - x = 3 \\ = > x + y = 15 \\ and \: x - y = 3 \: or \: y - x = 3$

Thus, we obtain the following systems of linear equations

$1) \: \: \: x + y = 15 \\ \: \: \: \: \: \: \: x \: - y \: = 3 \\ 2) \: \: x + y = 15 \\ \: \: \: \: \: \: y - x = 3$

Solving first systems of equations we get

$x = 9 \: and \: y = 6$

Solving second system of equations, we get

$x = 6 \: and \: y = 9$

Substituting the vaules of x and y in equation 1, we have

Number = 69 or, 96

Answer 2

Answer:

Hi Dear !

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Let the  No. Be xy 

ATGC , 

xy + yx               = 165 

10x + y + 10y+x = 165

11x + 11y           =  165

Divide Both sides By 11 

        x + y          =  15 __________(1)

Also,x - y           = 3 ____________(2) 

By 1 and 2 we get 

2x = 18 

x   =  9 

y   =  6

so the number is

So the number is 96 or 69 

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