Question

A two digit number is 4 times the sum of its two digits. The number that is formed by reversing its digits is 27 more than the original number. What is the number?
1. 27
2. 36
3. 42
4. 54

Answer 1

Correct Answer - Option 2 : 36

Let the tens and units digit of number are 'x', 'y' respectively

First condition:

10x + y = 4(x + y)

⇒ 10x + y = 4x + 4y

⇒ 10x - 4x = 4y - y

⇒ 6x = 3y

⇒ 2x = y        ----(1)

Second condition:

Reversed Number = (10y + x)

(10x + y) + 27 = 10y + x

⇒ 10x - x + y - 10y = -27

⇒ 9x - 9y = -27

⇒  9(x - y) = -27

⇒ (x - y) = -27/3

⇒ (x - y) = -3      ----(2)

Substitute the value of eq.1 in equation.2, we can get the value of x

x - 2x = -3

⇒ x = 3

Substitute the value of x in in eq.1, we can get the value of y

2 × 3 = y

⇒ y = 6

According to first condition the original number = 10 × 3 + 6

⇒ 36

Adding 27 to the first condition = 36 + 27

⇒ 63

According to the second condition the reversed number = 10 × 6 + 3

⇒ 6

∴ The original number is 36