Question

the sum of 2digit number is 11 the number obtained interchanging the digets exceeds the original number by 27. find the number

Answer 1

Let the unit digit be x and tens digit be y

x+y=11                 Eq 1

Number = 10y+x

Number after reversing digits = 10x+y

Given,

10x+y-(10y+x)=27

10x+y-10y-x=27

9x-9y=27 = 9(x-y)=27

x-y=3               Eq2

Adding Eq1 and Eq2

x+y+x-y = 11+3

2x=14

x=7

x+y=11

y=4

Number = 10y+x = 47

Answer 2

Let number = 10a + b (two digit)
Given, a + b = 11
a + 10b - 10a - b =27
Solving, a = 4, b= 7
Hence, number = 47