Question

The sum of the digits of a two digit number is 7 the number obtained by interchanging the digits exceed the original number by 27. find the no.​

Answer 1

Answer:

Let the unit place be x

Then, tens digit = 7 - x

original number = 10 ( 7 - x ) + x

= 70 - 10x + x = 70 - 9x

After interchanging of the digits, the resulting two digit number will be 10x + 7 - x

= 9x + 7

According to the question,

9x + 7 = 70 - 9x + 27

or, 9x + 9x = 97 - 7

or, 18x = 90

or, x = 90/18

x = 5

so, original number = 70 - 9x = 70 - 9 × 5

= 70 - 45 = 15

Answer 2

Let the units place be x . As sum of both the digits is 7 ,then the tens digit will be 7 - x .

Number formed by these digits = (10 x tens digit) + units digit

=> 10 (7 - x) + x

70x - 10x + x

70x - 9x

When the digits are interchanged then,

tens digit = x

units digit = 7 - x

The new no. formed = 10x + (7 - x)

= 9x + 7

Given that the no. exceeds by 27 with the original number .

New no. - Given no. = 27

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

9x + 7 - 70 + 9x = 27

18x - 63 = 27

18x = 63 + 27

18x = 90

x = 90/18

x = 5

Original number = 70 - 9x 

=> 70 - 45

=> 25