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If a certain number of two digits 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
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- 6
- 9
- 12
- 4
Correct Option: C
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 |
| ____________ |
| 3y = 15 |
| ⇒y = 5 |
From equation (ii),
2 × 5 – x = 3 ⇒ x = 10 – 3 = 7
∴ Sum of digits = x + y = 7 + 5 =12
