Question

a two digit number is such that the sum of its digit is 8 if 54 is subtracted from the number its digits are reserved find the number

Answer 1

Heya,
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Let unit digit be y .
Tens digit = x .
then , number = 10x + y .

The sum of digits is 8 so ,
x+y = 8   
x = y -8 .___________1.

then , 
10 x + y - 54 = 10 y + x 
putting 1 in equation.
 10 (8-y) +y -54 = 10y +(8-y)
80 -10y +y -54 = 10y +8-y 
-9y -9y = -18 
-18y = -18 
y = 1 

then x = 8-y 
x = 8-1 
x = 7 

then , Number = 10x + y 
                        = 10*7+1 
                        = 70+1
                         = 71 Ans.

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ANKIT