sum of digits of a two digit number is 9. also, the difference between this number and the number obtained by reversing the order of digits is 45. find the number.
Answers
Assume the digit in ones place as x and the digit in tens place is y The original number is (10y + x) Number obtained by reversing the digits = (10x + y) Now check for the condition Given that sum of digits of the number is 9 That is x + y = 9 → (1) Second condition is, number obtained by interchanging the digits is greater than the original number by 27 That is (10x + y) = (10y + x) 27 ⇒ 10x + y – 10y – x = 27 ⇒ 9x – 9y = 27 ∴ x – y = 3 → (2) Add (1) and (2), we get x + y = 9 x – y = 3 ----------- 2x = 12 ∴ x = 6 Put x = 6 in (1), we get 6 + y = 9 ⇒ y = 9 – 6 = 3 The original number = 10y + x = 10(3) + 6 = 36
Answer:
72
Step-by-step explanation:
let unit diigit be y and ten's digit be x
the require number is 10x+y
as per question,
(10x+y)-(10y+x)=45
i.e x-y=5
also we are given
x+y=9
i.e x=7, y=2
required no is 72