The unit digit of a two-digit number is 6. If 9 is added to the number, then the number obtained is `5//4th` of the number itself. Find the sum of the digits

Options

A. 7
B. 8
C. 9
D. 10

Answer

c

Explanation

Let the tens digit be x
Given, units digit be 6
`:. (10x + 6) + 9 = (5)/(4) (10x +6)`
`rArr 10x + 15 = (5)/(4) (10 x+6)`
`rArr 2x + 3 = (1)/(2) (5x + 3)`
`rArr 4x + 6 = 5x +3`
`rArr x = 3`
`:.` The sum of the digits `= 6 + 3 = 9`
Hence, the correct option is (c)