What will be the Sum of the Digits of the Number? If

A two digit number is 3 times the sum of its digits. If 45 is added to the number, its digits are interchanged. The sum of the digits of the number is:

  1. 9
  2. 8
  3. 5
  4. None of these
Sarif Default Asked on 31st July 2015 in Maths.
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1 Answer(s)

Answer:  (1) 9
Explanation:-
Let the number of two digits be = 10 X + Y
According to the question,
10 X + Y = 3 (X + Y)
10 X + Y = 3 X + 3 Y
10 X – 3 X = 3 Y – Y
7 X = 2 Y
7 X – 2 Y = 0                ……………………………………… (1)
According to second condition,
10 X + Y + 45 = 10 Y + X
10 X – X + Y – 10 Y  + 45 = 0
9 X – 9 Y = -45       …………………………………… (2)
Solve equation (1)  &  (2),
X = 2   &   Y = 7
Then, the number is 27
Hence, the sum of digits 2 + 7 = 9.

Anurag Mishra Professor Answered on 31st July 2015.
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