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Consider a two-digit number. The difference between the number and the number we get when its digits are reversed is 27. If the sum of the digits in the given number is 9, find the HCF of the number and the number when its digits are reversed.

Consider a two-digit number. The difference between the number and the number we get when its digits are reversed is 27. If the sum of the digits in the given number is 9, find the HCF of the number and the number when its digits are reversed. Correct Answer 9

Let the number be (10x + y)

According to the question

10x + y – 10y – x = 27

⇒ 9x – 9y = 27

⇒ x – y = 3      ----(i)

⇒ x + y = 9      ----(ii)

Add equation (i) and equation (ii)

2x = 12

⇒ x = 6

From equation (i)

y = 3

⇒ The number is = 63

The number when its digit reversed = 36

⇒ 63 = 3 × 3 × 7

⇒ 36 = 3 × 3 × 4

∴ HCF of 63 and 36 = 3 × 3 = 9

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