Question

The sum of a two-digit number and the number obtained by reversing the order of its digits is 121. Also, the difference of the units digit and the tens digit is 3. Then, the numbers are

• A. 62, 26
• B. 47, 74
• C. 41, 14
• D. 87, 78

Answer 1

The correct option is B 47, 74

Let the digit at the units place be x and the digit at the tens place be y. Then the number = 10y + x

From the condition given in the equation we have,
(10y + x) + (10x + y) = 121

$\Rightarrow$ 11(x+y)= 121 $\Rightarrow$ x + y = 11
and, x - y = 3 [ Differences of the units and the tens digits is 3]

Thus, we have the following sets of simultaneous equations
x + y = 11 ...(1)
x - y = 3 ...(2)

On solving equations (1) and (2), we get 2x = 11 + 3
$\Rightarrow$ x = 7

Substituiting x = 7 in equation (1), we get
7 + y = 11 $\Rightarrow$ y = 4
$\therefore$ When x = 7, y = 4.

Hence, the number = 10y + x = 10 $\times$ 4 + 7 = 47 and
reverse of the number = 10x + y = 10 $\times$ 7 + 4 = 74

Hence, the required numbers are 47 and 74.