Question

The two digit no is less by 1 than 6 times the sum of its digit The number obtained by interchanging the digit is less by 9 then the original number Find the original number​

Answer 1

Let the digits of number be x and y such that the number is 10x+y

Number obtained by interchanging the two digits of a two-digit number lesser than the original number by 54

10x+y -54 = 1oy+x

9x-9y = 54

x-y = 6 —-(1)

Sum of digits = 10

x+y= 10 ——(2)

By (1) and (2),

x = 8; y= 2

Verification:

Number = 82

Reversed no. = 28

Difference = 82–28 = 54 => OK

Ans: Original number is 82.

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