# A number consisting of two digits is seven times

A number consisting of a two digit number is 7 times the sum of its digit. when 27 is subtracted from the number the digits are reversed .find the number

Given : 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.

To find : the number.

As the number is a two digit , then let x be tens's place and y be one's place.

Therefore the two digit number would form as 10 x +y

according to the question,

a number consisting of two digits is 7 times the sum of its digits.

=> 10 x + y = 7( x+y)

=> 3x-6y=0

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

when 27 is subtracted from the number the digits are reversed.

After reversing the digits, the number = 10 y +x

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

=> 9 x- 9y = 27

=>x -y = 3 ...............(2)

Substituting the value of x from eq (1) to eq(2) , we get

=> 2y-y = 3

=> y = 3

x= 2y

=> x = 2(3) = 6

Therefore the number is =  10 (6) + 3 = 63

Answer : the required two digit number is 63

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