Question
In a two–digit number, the digit at the unit’s place is 1 less than twice the digit at the ten’s place. If the digits at unit’s and ten’s place are interchanged, the difference between the new and the original number is less than the original number by 20. The original number is
Answer: Option A
Answer: (a)Ten’s digit = x Unit’s digit = 2x – 1 Original number = 10x + (2x – 1) = 12x – 1New number = 10 (2x – 1) + x = 20x – 10 + x = 21x – 10(21x – 10) – (12x + 1) = 12x – 1 – 209x – 9 = 12x – 213x = 12 ⇒ x = 4Original number = 12x – 1 = 12 × 4 – 1 = 47
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Answer: (a)Ten’s digit = x Unit’s digit = 2x – 1 Original number = 10x + (2x – 1) = 12x – 1New number = 10 (2x – 1) + x = 20x – 10 + x = 21x – 10(21x – 10) – (12x + 1) = 12x – 1 – 209x – 9 = 12x – 213x = 12 ⇒ x = 4Original number = 12x – 1 = 12 × 4 – 1 = 47
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