Question

The sum of a two-digit number and the number

obtained by reversing the digits is 66. If the digits

of the number differ by 2, fnd the number.

Answer 1

Hello friend

Let one of the digits be x

According to the question, the other digit will be x+2

Number formed by x and x+2 is 10x+x+2=11x+2

(See this is like the expanded form. 72 is written as 7×10+2×1. In the same way the number whose tens digit is x and unit's digit is x+2 can be expressed as 10×x + x+2)

Number formed by reversing the digits will be 10×(x+2) + x

=10x+20+x

=11x+20
_________________________

By adding both the numbers we get 66

That is (11x+2)+(11x+20)=66

22x+22=66

22x=66-22

x=44/22

x=2

So the digits will be

x=2 and x+2=4

Number will be 24 and 42

Hope it helps!

Answer 2

let the two digit be x and y such that x>y.
then,
x-y=2
x=y+2 ---------1
(10x+y)+(10y+x) =66. ----------2
putting the value of 1 in 2.
we have
10y+20+y+10y+y+2=66
22y+22=66
y=3
therefore the no. is 53.
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