Question

the sum of a 2 digit number is 9 on revesing its digit the new number obtained is 45 more than the original number find the original number​

Answer 1

Answer = 27

1st condition

2 digit number = 10 x + y [ in tens place and y in ones]

sum of its digits => x+y = 9 -----------(1)

2nd Condition

when the numbers are reversed,

2 digit number = 10 y + x

Given it is 45 more than original,

==> ( 10 x + y ) + 45 = 10 y + x

==> 10 x - x + y - 10 y = -45

==> 9 x - 9y = -45

==> x - y = -5 ------------------------(2)

x + y = 9 _________(1)

x - y = -5_________(2)

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(1)+(2)=> 2x = 4

x = 2

substitute value of x in (1)

x + y = 9

2 + y = 9

y = 7

Digit = 20 + 7 = 27