# A number consisting of two-digits, is 7 times the sum of its digits. When 27 is subtracted from the number, the digits are reversed. Find the number.

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by dweejareddy

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by dweejareddy

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Let x is the tenth digit and y is unit digit.

then the number is 10x+y.

The number is 7 times the sum of the digits. So,

10x+y = 7(x+y)

⇒10x-7x = 7y-y

⇒3x = 6y

⇒x=2y

Also (10x+y)-27 = 10y+x

⇒10x-x = 10y-y+27

⇒9x = 9y +27

⇒9×2y = 9y + 27

⇒18y - 9y = 27

⇒9y = 27

⇒ y = 27/9 = 3

x = 2y = 6

The number is 10x+y =**63**

then the number is 10x+y.

The number is 7 times the sum of the digits. So,

10x+y = 7(x+y)

⇒10x-7x = 7y-y

⇒3x = 6y

⇒x=2y

Also (10x+y)-27 = 10y+x

⇒10x-x = 10y-y+27

⇒9x = 9y +27

⇒9×2y = 9y + 27

⇒18y - 9y = 27

⇒9y = 27

⇒ y = 27/9 = 3

x = 2y = 6

The number is 10x+y =

Digit in units place = y

The number is 10x + y

The number is 7 times its sum of digits

10x + y = 7(x+y)

10x + y = 7x + 7y

3x - 6y =0

3x = 6y

x = 2y .................(1)

If 27 is subtracted from the number, the digits are reversed.

10x + y - 27 = 10y + x

⇒ 9x - 9y = 27

⇒ x - y = 3 ........(2)

Solving equations (1) and (2)

We get, x = 6 and y = 3

The number is 63