Question

The sum of a two digit number and the number obtained by interchanging its digits of the number is $121$. If the digit of the number differ by $3$, find the number.

• A. $36,63$
• B. $45,54$
• C. $47,74$
• D. $57,75$

Answer 1

The correct option is C $47,74$

Let the digit at the unit's place $=x$

Let the digit at the ten's place $=y$

Then the 2-digit number is $=x+10y$ .............. (1)

On interchanging the digits of the number,

the digit at the unit's place $=y$

the digit at the ten's place $=x$

Then the new 2-digit number is $=y+10x$ .............. (2)

The sum of these two numbers is $121$

$x+10y+y+10x=121$

$11x+11y=121$

$11(x+y)=121$

$x+y=\frac{121}{11}$

$x+y=11$ ........................... (3)

The digits of the number differ by $3$

Case (1):

If $x>y$

Then,

$x-y=3$ ............. (4)

Adding (3) and (4),

$2x=11+3$

$2x=14$

$x=7$

then,

$y=11-x=11-7=4$

And the number is $=x+10y$

$=7+10\times 4$

$=7+40$

$=47$

Case (2):

If $y>x$

Then,

$y-x=3$ ............. (5)

Adding (3) and (5),

$2y=11+3$

$2y=14$

$y=7$

then,

$x=11-y=11-7=4$

And the number is $=x+10y$

$=4+10\times 7$

$=4+70$

$=74$