Question

Sum of 2 digits is9. If 27 is added to it,the number reverses. Find the number

Answer 1

let the number be xy

x+y=9...............(1)

(10x+y)+27=10y+x

10x-x+y-10y=-27

9x-9y=-27

x-y=-3................(2)

add equation 1 and 2

we get

x=3

substitute it in eq 1

y=6

so the number is 36

Answer 2

Let the no be x and 9-x

10×x+9-x

10x+9-x

9x+9

When we interchange the digits

10×9-x+x

90-10x+x

90+9x

Threfore,9x+9+27=90-9x

9+27-90=(-9x)(-9x)

54=(-18x)

54÷18=(-x)

3=x

9-x=6

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