-
By interchanging the digits of a two digit number we get a number which is four times the original number minus 24. If the unit’s digit of the original number exceeds its ten’s digit by 7, then original number is
-
- 29
- 36
- 58
- 18
Correct Option: A
Let the two–digit number be 10P + Q where P < Q.
Number obtained on reversing the digits =10Q + P
According to the question, 10Q + P = 4 (10P + Q) – 24
⇒ 40P + 4Q – 10Q – P = 24
⇒ 39P – 6Q = 24
⇒ 13P – 2Q = 8 .....................(i)
Again, Q – P = 7
⇒ Q = P + 7 ....(ii)
Put the value of Q from equation (ii) in equation (i).
∴ 13P – 2 (P + 7) = 8
⇒ 13P – 2P – 14 = 8
⇒ 11P = 14 + 8 = 22
| ⇒ P = | = 2 | |
| 11 |
From equation (ii),
Q – 2 = 7
⇒ Q = 2 + 7 = 9
∴ Number = 10Q + P = 10 × 2 + 9 = 29
