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A two digit number is five times the sum of its digits. If 9 is added to the number, the digits interchange their positions. The sum of digits of the number is :
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- 11
- 9
- 7
- 6
Correct Option: B
Let the two digit number be 10y + x.
According to the question,
10y + x = 5 (x + y)
⇒ 10y + x – 5x – 5y = 0
⇒ 5y – 4x = 0 ....(i)
And,
10y + x + 9 = 10x + y
⇒ 9x – 9y = 9
⇒ x – y = 1 ... (ii)
From equation (i),
⇒ 5y – 4(1 + y) = 0
[From (ii)]
⇒ 5y – 4 – 4y = 0
⇒ y = 4
∴ From equation (ii),
x = 4 + 1 = 5
∴ Number = 10 × 4 + 5 = 45
∴ Sum of digits = 4 + 5 = 9
