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Question

The sum of a two-digit number and the number obtained by reversing its digits is 99 and if digits differ by 3.Find the number.

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Solution

We have,
Case (I)-
1 unit place =x
10 unit place =y
10y+x

Case (II)
10 units place =x
1 unit place =y

y+10x
10y+x+y+10x=99
11y+11x=99
11(y+x)=99(I)
x+y=9
xy=3(II)

put the value (i)(ii)
2x=12
x=6

sum of two-digit number
36 or 63
Hence this is the answer.

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