Question

the sum of two no is 3 the no obtained by interchanging digit is 9 less than original number find original number

Answer 1

Hi there!
Here's the answer:


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In two digit No.,
Let Units digit be 'x'
and tens digit = '3-x's
( °•° Sum of the digits = 3 )


The 2-digit No. = 10x+(3-x)

Now,
The digits are interchanged

The New 2-digit No. has now (3-x) as tens digit and x as units digit

•°• New 2-digit No. = 10(3-x)+x


Given,
the New number= (Original Number) - 9

=> 10(3-x)+x = 10x+(3-x) - 9
=> 30-10x+x = 9x-6
=> -9x+30 = 9x-6
=> 18x = 36
=> x= 2

•°• Units digit of original No. x= 2
& tens digit of original No. 3-x= 3-2= 1

•°• Required 2-digit No. = 12

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Verification :

The No. = 12
Sum of digits = 3
Digits are Interchanged, New No. = 21
New No. - Old No.= 9
21- 12 = 9

•°• Given Data matched.

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:)
Hope it helps