Question

The digits of a two digit no differ by 7. If the digits are interchanged and the resulting no is added to the original no we get 121. Find the original no

Answer 1

Given xy be the required two digit number.

Let the digit in ten's place be x.

Let the digit in one's place be y.

Therefore the required number is 10x+y.    ------ (*)

Given that the digits of a two digit number differ by 7.

x - y = 7   ----- (1)

Given that if the digits are interchanged and the resulting number is added to the original number we get 121.

10x + y + 10y + x = 121

11x + 11y = 121

x + y = 11 -------------- (2).


On solving (1) & (2), we get

x + y = 11

x - y = 7

--------------

2x = 18

x = 9

Substitute x = 9 in (1), we get

x + y = 11

9 + y = 11

y = 11 - 9

y = 2.


Substitute x & y in (*), we get

The original number = 10(9) + 2

                                   = 90 + 2

                                   = 92.


Hope this helps!

Answer 2

Answer:

Given:

x-y=7 {as they differ by 7}

Let the original two-digit number be 10x + y

given,sum of two digit number=121

When interchanged,

10x+y+10y+x=121

Step-by-step explanation: