A two digit number is 5 times the sum of its digits. The number is:

1. 63

2. 36

3. 45

4. 54

45

Reason

Let the two digit number be 10x + y.

It is given that two digit number is 5 times the sum of its digits

⇒ 10x + y = 5(x + y)

⇒ 10x + y = 5x + 5y

⇒ 10x - 5x = 5y - y

⇒ 5x = 4y

⇒ y = $\dfrac{5}{4}$x

As x and y are digits, so

x ∈ {1, 2, 3, 4, 5, 6, 7, 8, 9}

and

y ∈ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

Since y must be a single digit integer, x must be a multiple of 4. The only possible values for x from the above set are x = 4 and x = 8.

For x = 4, y = $\dfrac{5}{4} \times$ 4 = 5

For x = 8, y = $\dfrac{5}{4} \times$ 8 = 10 which is not a valid digit.

∴ Valid digits are x = 4 and y = 5.

∴ The number = 10 × 4 + 5 = 45

Hence, option 3 is the correct option.