Question

The sum of a two digit number and the number obtained by reversing the digits is 121 and the two digits differ by 3. Find the number.

• A. 62 or 26
• B. 47 or 74
• C. 41 or 14
• D. 87 or 87

Answer 1

The correct option is B

47 or 74

Let the digits at the unit's place be x and the digit at the tens place be y. Then,
Number = 10y + x
From first condition
(10y + x) + (10x + y) = 121
$\Rightarrow$ 11(x+y)= 121 $\Rightarrow$ x + y = 11
and, x - y = $\pm$ 3 [ Differences of digits is 3]
Thus, we have the following sets of simultaneous equations
x + y = 11 . . . (1) x - y = 3 . . . (2)
x + y = 11 . . . (3) x - y = -3 . . . (4)
On solving equations (1) and (2), we get
x + y = 11
x - y = 3
$\Rightarrow$ 2x = 11 + 3
$\Rightarrow$ x = 7
Substituiting x = 7 in equation (1)
7 + y = 11 $\Rightarrow$ y = 4
$\therefore$ When x = 7, y = 4, we have
Number = 10y + x = 10 $\times$ 4 + 7 = 47
On solving equations (3) and (4), we get
x + y = 11
x - y = -3
$\Rightarrow$ 2x = 11 - 3
$\Rightarrow$ x = 4
Substituiting x = 4 in equation (3)
4 + y = 11 $\Rightarrow$ y = 7
$\therefore$ When x = 4, y = 7, we have
Number = 10y + x = 10 $\times$ 7 + 4 = 74
Hence, the required number is either 47 or 74