Summation of unit place and ten place digits of a number is 9. After interchanging the digits the difference between the earlier and present numbers is 9. What is the number?

Correct option is C

Let unit place’s digit be x

Tenth place’s digit be (9 – x)

Number = 10 (9 – x) + x = 90 – 10x + x = 90 – 9x

After changing places, the number = 10x + (9 – x) = 10x + 9 – x = 9x + 9 

ATQ,

(90 – 9x) – (9x + 9) = 9

90 – 9x – 9x – 9 = 9

81 – 18x = 9

18x = 72

x = 4 

Number = 90 – 9x = 90 – 9(4) = 90 – 36 = 54