the sum of the digits of a 2-digit number is 7.if the digits are reversed, the new number is incresed by 3 less than 4 times the original number. find the original number

 

 

 

Asked by khare.shubhangi | 19th Feb, 2018, 01:20: PM

Expert Answer:

begin mathsize 16px style Let space the space digit space at space unit apostrophe straight s space place space be space straight x space and space digit space at space ten apostrophe straight s space place space be space straight y.
Then comma space original space number equals 10 straight x plus straight y

Sum space of space digits equals 7
rightwards double arrow straight x plus straight y equals 7 space space space space space space space..... left parenthesis 1 right parenthesis

Also comma space 10 straight y plus straight x equals 4 left parenthesis 10 straight x plus straight y right parenthesis minus 3
rightwards double arrow 10 straight y plus straight x equals 40 straight x plus 4 straight y minus 3
rightwards double arrow 39 straight x minus 6 straight y equals 3
rightwards double arrow 13 straight x minus 2 straight y equals 1 space space space space space space.... left parenthesis 2 right parenthesis

Multiplying space equation space left parenthesis 1 right parenthesis space by space 2 comma space we space get
2 straight x plus 2 straight y equals 14 space space space space space space..... left parenthesis 3 right parenthesis

Adding space equations space left parenthesis 2 right parenthesis space and space left parenthesis 3 right parenthesis comma
15 straight x equals 15
rightwards double arrow straight x equals 1
rightwards double arrow straight y equals 6
Hence comma space the space original space number equals 10 straight x plus straight y equals 10 left parenthesis 1 right parenthesis plus 6 equals 16 end style

Answered by Rashmi Khot | 19th Feb, 2018, 02:10: PM