Question

a number consisting of two digits is equal to 7 times the sum of its digits.When 27 is subtracted from the number, the digita interchange their places. find the number

Answer 1

Hey

Here is your answer,

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

Hope it helps you!