If a certain number of two digit is divided by the sum of its digits, the quotient is 6 and the remainder is 3. If the digits are reversed and the resulting number is divided by the sum of the digits, the quotient is 4 and the remainder is 9. The sum of the digits of the number is

A. 6

B. 9

C. 12

D. 4

Answer: Option C

Solution(By Examveda Team)

Let the number be 10x + y
Dividend = Divisor × Quotient + Remainder
∴ 10x + y = 6(x + y) + 3
⇒ 10x + y = 6x + 6y + 3
⇒ 10x - 6x + y - 6y = 3
⇒ 4x - 5y = 3 . . . . . . (i)
Again, 10y + x = 4(x + y) + 9
⇒ 10y + x = 4x + 4y + 9
⇒ 6y - 3x = 9
⇒ 2y - x = 3 . . . . . . (ii)
∴ By equation (i) + 4 × (ii),
4x - 5y = 3
8y - 4x = 12
$$\overline {3{\text{y}}\,\,\,\,\,\,\,\,\, = 15} $$
⇒ y = 5
From equation (ii)
2 × 5 - x = 3
⇒ x = 10 - 3
⇒ x = 7
∴ Sum of digits = x + y = 7 + 5 = 12