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A number consists of two digits such that the digit in the ten’s place is less by 2 than the digit in the unit’s place. Three times the number added to 6/7 times the number obtained by reversing the digits equals 108. The sum of digits in the number is :
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- 8
- 9
- 6
- 7
Correct Option: D
Let the unit’s digit be x.
∴ Ten’s digit = x – 2
∴ Number = 10 (x – 2) + x
= 10x – 20 + x = 11x – 20
New number obtained after reversing the digits
= 10x + x – 2 = 11x – 2
According to the question
| 3(11x − 20) + | (11x – 2) = 108 | |
| 7 |
| ⇒ (11x − 20) + | (11x – 2) = 36 | |
| 7 |
⇒ 77x – 140 + 22x – 4 = 252
⇒ 99x = 252 + 144
| ⇒ x = | = 4 | |
| 99 |
∴ Number = 11x – 20
= 11 × 4 – 20 = 24
∴ Sum of digits = 2 + 4 = 6
