Question

the difference of the digits of a 2 digit number is 3. if the digits are interchanged and the new number is added to the original number, the result is 77. find the original number

Answer 1

Answer:

52 or 25

Step-by-step explanation:

Let the ten's digit be 'x' and unit's digit be 'y'.

Then, it is given

x - y = 3... [equation i]

Now, the original number = 10x + y

Number obtained by interchanging its digits = 10y + x

Now, according to the question, the sum of both the numbers is 77

=>> 10x + y + 10y + x = 77

=> 11x + 11y = 77

=> 11 (x + y) = 77

=> x + y = 77/11

=> x + y = 7... [equation ii]

Now, adding equations i and ii,

x - y = 3

x + y = 7

(+) (+) (+)

=> 2x = 10 (y and -y get cancelled)

=> x = 10/2

=> x = 5

•°• x = 5

Now, substituting the value of x in equation i,

x - y = 3

=> 5 - y = 3

=> 5 - 3 = y

=> 2 = y

•°• y = 2

Therefore, original number,

= 10x + y

= 10(5) + 2

= 50 + 2

= 52

And, number obtained by interchanging its digits,

10y + x

= 10(2) + 5

= 20 + 5

= 25

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The number is 52,

• Difference between the number,

= 5 - 2

= 3

• Sum of original number and number obtained by interchanging the digits,

= 52 + 25

= 77.

Hence verified.

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