A two-digit number is 12 more than five times the sum of its digits. The number formed by reversing the digits is 9 less than the original number. The number is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 87.
Let the number be xy
Can be written as 10x + y.
We know,
10x + y = 5(x + y) + 12
10y + x = 10x + y - 9
According to the question;
⇒ 10x + y = 5(x + y) + 12
⇒ 10x + y = 5x + 5y + 12
⇒ 5x - 4y = 12 ------- (1)
Similarly,
⇒ 10y + x = 10x + y - 9
⇒ y - x = -1 ---- (2)
Solving equation (1) and (2),
⇒ x = 8 and y = 7
Hence, the required number = 10x + y = 10 × 8 + 7
⇒ 80 + 7 = 87