Question

the sum of the digits of a two digit number is 10 and if 18 is subtracted from it the digits in resulting number are same find the number

Answer 1

Let the Ten's digit be x and Unit's digit be y
ORIGINAL NUMBER = 10x + y

ACCORDING TO QUESTION,

x + y = 10 -------------(i)

10x + y - 18 = 10y + x ---------(ii)

Solving (ii)
9x - 9y = 18
Dividing by 9

x - y = 2 ----------- (iii)

ADDING (i) & (iii)

x + y = 10
x - y = 2
_____________
2x = 12

x = 6

Substituting x in eq (i)
6 + y = 10

y = 4

ORIGINAL NUMBER = 10x + y
=> 10 × 6 + 4
=> 64

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ANSWER = 64
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