A two-digit number is 4 times the sum of its digits. If the digits are reversed, the new number is 27 more than the original. What is the number?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 36.
Let the number be 10x + y
Given: 10x + y = 4(x + y)
10x + y = 4x + 4y
6x = 3y
y = 2x
So one’s digit is double the ten’s digit.
Now, when digits are reversed:
New number = 10y + x
And it’s 27 more than the original:
10y + x = 10x + y + 27
9y − 9x = 27
y − x = 3
From before, y = 2x
So 2x − x = 3 ⇒ x = 3
Then y = 6
Hence, the number = 36