Question

The sum of two digit number is 17. If the number formed by reversing the digits is less than the original number by 9,find the original number.

Answer 1

QUESTION.

The sum of the digit of a two digit number is 17.

if the digit is formed by reversing the digit is less than the original number by 9 . find the

original number

To find the original number,

EXPLANATION.

Let tens place digit = x

Let unit place digit be = y

original number = 10x + y

reversing number = 10y + x

according to the question,

sum of digit of two digit number = 17

x + y = 17 ....(1)

digit is formed by reversing the digit is less than the original number = 9

10x + y - 9 = 10y + x

9x - 9y = 9

x - y = 1 ....(2)

From equation (1) and (2) we get,

2x = 18

x = 9

put the value of x = 9 in equation (1) we get,

9 + y = 17

y = 8

Therefore,

Original number = 10x + y

10(9) + 8 = 98

original number = 98

Answer 2

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The number is 98.

Let the two digits be x, and y. The given conditions are:

(x+y) = 17 ...... ( i )

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

So:

10y-y+x-x=10x-x+y-y+9

9y/9 = 9x/9 + 9/9

y=x+1

If the sum of the digits (x+y) equals 17, then:

x+x+1=17

2x+1 = 17–1

2x/2 = 16/2

x = 8, and y = 9 【(8+9=17)】

Verification :

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

10(9)+8 = 10(8)+9+9

98 = 89+9

So the number is 98.

Verified ✅.

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