Q. 18

# The sum of a two - digit number and the number obtained by reversing the order of its digits is 121, and the two digits differ by 3. Find the number.

Let the two - digit number be xy (i.e. 10x + y).

After reversing the digits of the number xy, the new number becomes yx (i.e. 10y + x).

According to question -

(10x + y) + (10y + x) = 121

11x + 11y = 121

x + y = 11.....(1)

and,

x - y = 3 or y - x = 3

[as we don't know which digit is greater out of x and y]

x - y = ±3.....(2)

Adding Equation (1) and (2), we get -

2x = 14 or 8

x = 7 or 4

Case 1. when x = 7

y = 4 [from equation (1)]

Case 2. when x = 4

y = 7 [from equation (1)]

Thus, the possible numbers are 47 or 74.

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