The sum of the digits of a two-digit number is 9. The number obtained by reversing its digits is greater than the original number by 27. Which of the following statements are correct?
(A) The number is 36.
(B) The number is a perfect square.
(C) The product of the digits of the number is 20.
(D) The number obtained by reversing the digits is 63.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A), (B) and (D) only
Let the tens digit be \(t\) and the units digit be \(u\). The number is \(10t + u\) and the reversed number is \(10u + t\).
\(t + u = 9\)
\((10u + t) - (10t + u) = 27\)
\(9(u - t) = 27\), so \(u - t = 3\)
\(u = 6\), \(t = 3\)
So the number is 36, its reversed number is 63, and the product of its digits is 18.
Checking the statements
(A) The number is 36. — Correct. \(3 + 6 = 9\) and \(63 - 36 = 27\).
(B) The number is a perfect square. — Correct. \(36 = 6^{2}\).
(C) The product of the digits of the number is 20. — Incorrect. \(3 \times 6 = 18\).
(D) The number obtained by reversing the digits is 63. — Correct. Reversing 36 gives 63.