Question : By interchanging the digits of a two-digit number, we get a number that 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 the original number is:
Option 1: 29
Option 2: 36
Option 3: 58
Option 4: 18
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Correct Answer: 29
Solution : Let the original number be (10P + Q) and its reversed number be (10Q + P). By interchanging the digits of a two-digit number, we get a number that is four times the original number minus 24. (10Q + P) = 4 × (10P + Q) – 24 ⇒ 39P – 6Q = 24 ⇒ 13P – 2Q = 8 .....................(i) Again, Q – P = 7 ....................(ii) Solving equation (i) and equation (ii), We get, P = 2 and Q = 9 The original number is 10P + Q = 10 × 2 + 9 = 29 Hence, the correct answer is 29.
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