Question

the sum of the digits of a two digit number is 7 . the number got by interchanging the digits is 27 more than the original number.what is the number? ​

Answer 1

ANSWER:-

Let the unit digit be x

Tens digit = 7-x

Original no. = 10(7-x) +x×1

= 70-10x+x

= 70-9x

After inter changing

Units digit = 7-x

Tens digit = x

New no. = 10×x +1(7-x)

= 10x+7-x

= 9x+7

By condition,

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

9x+7-70+9x = 27

18x-63 = 27

18x = 27+63

18x = 90

x = 90/18

x = 5

Original no. = 70-(9×5) = 70-45 = 25

New no. = 9×5 +7 = 45+7 = 52