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The product of digits of a 2-digit number is 24. If we add 45 to the number, the new number obtained is a number formed by interchanging the digits.What is the original number?
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- 54
- 83
- 38
- 45
- 54
Correct Option: C
Let the two digit number be 10p + q.
According to the question,
pq = 24 .... (i)
and, 10p + q + 45 = 10q + p
⇒ 10q + p – 10p – q = 45
⇒ 9q – 9p = 45
⇒ 9(q – p) = 45
| ⇒ q − p = | = 5...(ii) | |
| 9 |
∴ (p + q)2 = (q – p)2 + 4pq
(p + q)2 = 52 + 4 × 24
(p + q)2 = 25 + 96 = 121
⇒ p + q = √121 = 11 ... (iii)
On adding equations (ii) and (iii),
q – p + p + q = 5 + 11
⇒ 2q = 16 ⇒ q = 8
∴ pq = 24 ⇒ 8p = 24
| ⇒ p = | = 3 | |
| 8 |
∴ Required number = 10p + q = 10 × 3 + 8 = 38
