Question

The difference of the digits of a two digit number is 2.the sum of the number and the number obtained by reversing the digits is 66.find the number

Answer 1

Let the digits be x and y
Given x - y = 2 ......(i)

When writing as number we write as
10x + y
The given two digits number is 10x + y

Now given reverse + original =66

Reverse of 10x + y = 10y + x

=> 10x + y + 10y + x = 66
=> 11x + 11y = 66

=> 11(x + y) = 66
=> x + y = 66/11
=> x + y = 6 .......... (ii)


Adding (i) and (ii)
x - y + x + y = 2 + 6
=> 2x = 8
=> x = 8/2
=> x = 4


Now substituting the value of x in (i) we have

x - y = 2
=> 4 - y = 2
-y = 2 - 4
- y = (-2)

=> y = 2


So the digit is
10x + y
=> 10 × 4 + 2
=> 40 + 2
= 42


Hence the digit is 42


Hope it helps dear friend ☺️✌️✌️

Answer 2

Let ten's digit be = y
and one's digit be = x
so the number = 10y+x

According to 1st condition,
y - x = 2 ---------(eqn.1)
so y= 2 + x --------(eqn.2)

According to 2nd condition,
(10x+y) + (10y+x) = 66

From eqn.2,
10x+2+x+10(2+x)+x=66
12x+2+20+10x = 66
22x= 66-22
x = 44/22
x=2
Putting the value of x in eqn.2 , we get
y= 4

Thus the required answer is
10y+x= 10×4+2
= 42
hope will help u