# 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:

- 9
- 8
- 5
- None of these

**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.