Question

The digits of a two digit number differ by 5. If the digits are interchanged and the resulting number is added to the original number, we get 99. Find the original number.

Answer 1

Let the number be 10y+x

x-y=5........(1)

10x+y+10y+x=99

11x+11y=99

x+y=9........(2)

From (1),x=5+y

Put (1) in (2)

5+y+y=9

5+2y=9

2y=4

y=2

So,x=5+2=7

Original number=27

Answer 2

HeRe Is Your Ans ⤵

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Let the one digit number be x

And tens digit number be y

(y > x)

Number = 10y + x

And interchanged number = 10x + y

According to the question,

=> x - y = 5 ------- 1

=> 10y + x + 10x + y = 99

=> 11y + 11x=99

=> x + y = 9 -------- 2

Subtract equation 1 and 2

=> x + y - ( x - y ) = 9 - 5

=> 2y = 4

=> y = 2

Putting y = 2 in equation 1

=> x - y = 5

=> x - 2 = 5

=> x = 7

Hence , The original number is

10y + x =10 × 2 + 7 = 27

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