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A 2-digit number is 3 times the sum of its digits. If 45 is added to the number, its digits are interchanged. The sum of digits of the number is
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- 11
- 9
- 7
- 5
Correct Option: B
Let the two digit number be = 10x + y.
According to the question,
10 x + y = 3(x + y)
⇒ 10 x + y = 3x + 3y
⇒ 10 x + y – 3x –3y = 0
⇒ 7 x – 2y = 0 ....(i)
and,
10 x + y + 45= 10 y + x
⇒ 10 y + x – 10x –y = 45
⇒ 9 y – 9 x = 45
⇒ 9 (y – x) = 45
⇒ y – x = 5 ...(ii)
2 × (ii) + (i) we have
2y –2x + 7x – 2y =10
| ⇒ 5x = 10 ⇒ x = | = 2 | |
| 5 |
From equation (ii),
y –2 = 5 ⇒ y = 2 + 5 = 7
∴ Number = 10x + y
= 2 × 10 +7 = 27
∴ Sum of digits = 2 + 7 = 9
