Q13 of 54 Page 77

The digits of a two - digit number differ by 3. If the digits are interchanged and the resulting number is added to the original number we get 143. What can be the original number?

A 2 digit number can be expressed as 10 x + y, where x is the ten’s digit and y is the unit digit. For example:

16 = 1(10) + 6


It is given that the digits differ by 3


x – y = 3 ……(1)


When digits are interchanged, resulting number will be 10x + y


Resulting number + Original number = 143


10y + x + 10x + y = 143


11y + 11x = 143


11(x + y) = 143


x + y = 13 ……(2)


Eliminate (1) and (2) by adding both the equations


x – y = 3


x + y = 13


2x = 16


x = 8


Put x = 8 in (1)


8 – y = 3


y = 5


Original number = 10x + y


= 10×8 + 5


= 80 + 5


= 85


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