Question

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 121.Find the original number.

With suitable explanation

Answer 1

Answer:

74, 47 (two answers possible)

Step-by-step explanation:

Let the tenths place digit be x and once place be y.

Original number=10(x)+1(y)

=10x+y

Interchanging digits of number=10(y)+1(x)

= 10y+x

According to question,

10y+x+10x+y=121

11x+11y=121

11(x+y)=121

x+y=11----------1

Case 1

If x >y

Then x-y=3--------------2

Adding 1 & 2

x+y+x-y=11+3

2x=14

x=7

7-y=3(from 2)

y=7-3

y=4

Thus, number is 74.

Case 2

If y>x

Then y-x=3--------------3

Adding equation 1&3

x+y+y-x=11+3

2y=14

y=7

7-x=3

x=7-3

x=4

Thus, number is 47

In this type of question, two answers are possible.