Question

The sum of a two number and the number obtained by reversing the digits is 99 if the number obtained by reversing the digits is 9 more than the original number find the number

Answer 1

Let the 2 digit no. be 10x+Y

According to the question

(10x+y)+(10y+x)=99

10x+y+10y+x=99

11x+11y=99

11(x+y)=99

x+y=99/11

x+y=9_____(1)

Then,

10y+x=(10x+y)+9

10y+x-(10x+y)=9

10y+x-10x-y=9

9x-9y=9

9(x-y)=9

x-y=1_____(2)

Solving (1) and (2)

x+y=9

x-y=1

》2x=10

x=5

Substituting x=5 in (1)

5+y=9

y=4

The no.=10(5)+4=54

Ans: The no. is 54

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