In a two-digit number the units digit is three less than the tens digit. If the digits are reversed, the sum of the reversed number and the original number is 121. Find the original number.

74.

Step-by-step explanation:

Let the number be xy.

Then from the given data

x = y + 3 ... (1)

The numerical value of xy is 10x + y so the second equation is

10x + y + 10y + x = 121

11x + 11y = 121 Simplifying:

x + y = 11

x = - y + 11 ... (2) Adding equations (1) and (2):

2x = 14

x = 7

and therefore y = 7 - 3 = 4.

74

Step-by-step explanation:

Lets try with numbers. Note that, as we need that the 2-digit number and its reverse sum 121 we can not use a very small number as, for example, 30.

Lets try with 52, where 5 = 3+2, so it fits.

its reverse is 25 and 52 + 25 = 77. So, is not 52.

The next is 63. Its reverse is 36. 36+63 = 99. So, is not 63.

The next is 74. Its reverse is 47. 74 + 47 = 121. Bingo!

The number is 74!