Question

the sum of a two digit number and the number formed by interchanging it's digit is 110.if 10 is subtracted from the original number, the new number is 4 more than 5 times the sum of digit of the original number. find the original number​

Answer 1

Answer: 64

Step-by-step explanation:

let a be the tens digit and b be the ones digit of the original number

Then the number is 10a+b

when the digits are interchanged we get the number 10b+a

So (10a+b) + (10b+a)=110

⇒ 11a + 11b = 110

⇒11 (a+b)=110

⇒a+b=10.......(1)

Also given, if 10 is subtracted from the original number, the new number is 4 more than 5 times the sum of digit of the original number

10a+b-10=5(a+b)+4

⇒10a + b - 5a - 5b = 4+10

⇒5a - 4b = 14.........(2)

Multiplying (1) by 5, we get

5a + 5b = 50 ...........(3)

(3)-(2).......>

9b = 36

⇒ b=4

from (1) a=6

So the original number is 64

Answer 2

THE VALUE OF ORIGINAL NUMBER IS 46