Question

The sum of the digits of a two digit number is 11 the number got by interchanging the digits is 27 more than the original number.What is this number​

Answer 1

Let the units place be x

then the tens digit be 7 - x

number formed by these digits = 10 x t's digit+u's digit

=> 10(7-x)+x

70 x -10 x +x

70 x -9x

when the digits are interchanged than,

t's digit= x

u's digit = 7-x

the new no. formed = 10x + 7-x

= 9 x +7

given that the no. exceeds by 27

new no. - given no.

9x +7 - (70-9x)=27

9 x + 7 - 70 + 9x =27

18x -63= 27

18 x = 63+27

18 x= 90

x = 90/18

=5

the no. = 70- 9x

=> 70-45

=> 25 ans

verify : 2+5 = 7

Answer 2

Heya!!

Let the digits of that two digit number be x and y

According to the given question.

x + y = 11 ... Equation ( i )

This two digit number can be written like this 10x + y

When we interchange the digits the new number becomes 10y + x

According to the given address question

10y + x = 27 + 10x + y

9y - 9x = 27

y - x = 3 ... Equation ii

Now, Add both the Equations we have

2y = 14

y = 7

Put value of y in Equation i we have

x + 7 = 11

x = 4

So, the two digit number is 47