Question

The digits of the two- digit number differ by 3. If the digits are interchanged and the resulting number added to the given number, the sum is 143. What is the original number.


Do it with solution

Answer 1

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let, the the unit digit is =X

and the 2'nd place digit is =Y

where,X>Y(let)

therefore, the original number is =(10Y+X)

now....

X=Y+3...........(I)

therefore, the original number is

=(10Y+Y+3)=(11Y+3) [putting,X=Y+3]

now.....the digita are interchanged....

therefore ,the new number would be

=(10X+Y)

=(10Y+30+Y) [putting,X=Y+3]

according to the question:If the digits are interchanged and the resulting number added to the given number, the sum is 143.

so.....

=>(10Y+30+Y) +(11Y+3)=143

=>11Y+30+11Y+3=143

=>22Y=110

=>Y=110/22

=>Y=5

therefore, X=5+3=8

therefore,.......

the original number is

=(11×5)+3

=58

$\large\mathcal\red{hope\: this \: helps \:you......}$