Question

Sum of the digit of a two-digit number is 9.when we interchange the digits,it is found that the resulting new number is greqter than the original number by 27. What is the two digit number

Answer 1

X + Y = 9

X = 9 - Y - eq. 1

Given :

(10Y + X) - (10X + Y) = 27

10Y + X - 10X - Y = 27

9Y - 9X = 27

Divide the entire equation by 9

Y - X = 3

From eq. 1 we know, X = 9 - Y

Thus,

Y - (9 - Y) = 3

Y - 9 + Y = 3

2Y = 3+ 9

2Y = 12

Y = 12/2 = 6

From eq. 1,

X = 9 - Y

X = 9 - 6

X = 3

Therefore,

The no. is 10X + Y

= 36

Hope it helps :)

Answer 2

Hey friend,

Here is the answer you are searching for,

Let the digits be x,y

Given,

x+y = 9

=> y = 9-x

Let the original number be (10y + x),

New number be (10x + y),

Also given,

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

By taking y as (9-x),

=> 10(9-x)+x+27 = 10x+9-x

=> 90-10x+x+27 = 9x+9

=> 117-9x = 9x+9

=> 18x = 108

=> x = 108/18 = 6

=> y = 9-6 = 3

Therefore,

Digits = 3,6

=> Original number = 36

HOPE IT HELPS YOU.

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