Question

The sum of digits of two digit number is 13 if the digits are interchanged and the resulting number is added to original number then we get 143 what is the original number​

Answer 1

Answer:

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Let ab represent the required 2 digit number.

Now,according to question,we get 2 equations:

a+b=13———-(1)

Now,

The value of the number is =10a+b (for eg the the number 13 can be represented as (10 ×1)+3)

And the value of the interchanged number is=10b+a

According to question:

(10a+b)+(10b+a)=143

=》10a+10b+a+b=143

=》10(a+b)+(a+b)=143

=》10(13)+(13)=143(from equation 1)

=》143=143

the equation of the above form shows that the relationship is true for all a+b=13(ie-equation 1)

Now,a+b=13 for:

a=4;b=9

a=5;b=8

a=6;b=7

a=7;b=6

a=8;b=5

a=9;b=4

So the original numbers are:

49,58,67,76,85,94