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.

Answer : 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