The sum of the digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 18. Find the number.

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answer is B.

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Detailed Solution

Let unit and tens digit be x and y.

∴ Original number = 1x + 10y …(i)

Reversed number = 10x + 1y

According to question,

x + y = 8

⇒ y = 8 – x …(ii)

Also, 1x + 10Oy – (10x + y) = 18

⇒ x + 10y – 10x – y = 18

⇒ 9y – 9x = 18

⇒ y – x = 2 …[Dividing both sides by 9] —-(iii)

⇒ 8 – x – x = 2 …[From (iii)]

⇒ 8 – 2 = 2x

⇒ 2x = 6

From (it), y = 8 – 3 = 5

From (i), Original number = 3 + 10(5) = 53

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