Question

A 2 digit number is formed by either subtracting 16 from 8 times the sum of the digits
or by adding 20 to 22 times the difference between difference of digits.find the number?

Answer 1

HI !

Let the digit in one's place be y and in ten' s place be x
The no: is 10x + y

sum of digits = x + y 

given .
10x + y = 8(x+y) - 16
10x + y = 8x + 8y  -16

2x - 7y = -16                           -----> [1]

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also ,

difference of digits = x - y                          [ x > y ]

10x + y = 22(x - y) + 20

10x + y = 22x - 22y + 20

22x - 10x - 22y - y = -20

12x - 23y = -20                    ----> [ 2]

solving equations 1 and 2 ,
6(2x - 7y = -16 ) = 12x - 42y = -96

   12x - 23y = -20  
- 12x - 42y = -96
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19y  = 76
y = 76/19 = 4

to get the value of x , put this value in any equation .
2x - 7y = -16   
2x - 28 = -16

2x = 12
x = 6

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x = 6 . y = 4

the no: is 10x + y

10 x 6 + 4 = 64

64 is the no: