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# 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.

Asked by 18th July 2012, 10:44 PM
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
Answered by Expert 19th July 2012, 12:03 AM
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