Question

the sum of the digits of a two -digit number is 7. the number is obtained by interchanging the digits exceeds the original number by 27 . find the number

Answer 1

Heya

Let the number be xy where x is the ten's digit and y is the unit's digit.

x+y=7......(1)

It can be written as 10x+y

[23 can be written as 10×2+3=20+3]


If the digits are reversed, the number becomes yx i.e 10y+x

According to the problem,

10y+x=10x+y+27

10y-y+x-10x=27

9y-9x= 27

-9(x-y)=27

x-y= 27/-9

x-y= -3......(2)

(1) + (2)

x+y=7
x-y=-3
---------
2x=4

x=4/2

x=2

Substituting x=2 in eq (1)

x+y=7

2+y=7

y=5

The number is 25