Question

sum of the digits of a two-digit number is 9. when we interchange the digits, it is found that the resulting new numbers is greater than the original number by 27. what is the two-digit number?​

Answer 1

Answer:

The original number is 36.

Step-by-step explanation:

Let the number be xy. So the general form is 10x + y.

The interchanged number will be yx or 10y + x. ATQ,

x + y = 9

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

x + y = 9

9y - 9x = 27

x + y = 9

y - x = 3

x + y = 9

x - y = -3. By eliminating x,

2y = 12

y = 6.

So x = -3 + 6 = 3.

So the original number is 36.

Verification : 3 + 6 = 9, and 63 - 36 = 27!

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Answer 2

Let the ones digit be x.

As the sum is 9,

the tens digit = (9-x)

According to condition,

{10x+(9-x)}-{10(9-x)+x} = 27

or, (9x+9)-{(90-10x)+x}= 27

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

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

or, 18x-81 = 27

or, 18x = 27+81

or, 18x = 108

or, x = 108/18

or, x = 6

So, ones digit = x = 7

and tens digit = (9-x) = 9-6 = 3

Hence, the two-digit number is 36.

Verify-

• 6+3 = 9
• 63-36 = 27

or, 27 = 27

Hence, L.H.S = R.H.S.