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In a two-digit number, the digit at unit’s place is less than the digit at the tenths place by 2. If the digits at the unit place and the tenth place are interchanged, the difference between the newly formed number and the original number is three times the digit at the unit place in the original number. What is the original number?

In a two-digit number, the digit at unit’s place is less than the digit at the tenths place by 2. If the digits at the unit place and the tenth place are interchanged, the difference between the newly formed number and the original number is three times the digit at the unit place in the original number. What is the original number? Correct Answer 86

Given:

Digit in the unit’s place is less than the digit at the tenths place by 2

Calculation:

Lat the digit at tenth place be x

⇒ Digit at unit place = x – 2

Number formed = 10x + x – 2 = 11x – 2

On interchanging the digits,

New number formed = 10(x – 2) + x = 11x – 20

According to the question,

(11x – 2) – (11x – 20) = 3(x – 2)

⇒ 18 = 3x – 6

⇒ 3x = 24

⇒ x = 8

∴ Required number = 11x – 2 = 11 × 8 – 2 = 88 – 2 = 86

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