A no. Consists of two digit . When it is divided by the sum of the digits , the quotient is 7 . The sum of the recipocals of the digit is 9 times the product of the recipocals of the digits . Find the no.
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21
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Let our number of two digits = xy
Then
From first condition , we get
xyx + y = 7 ------------------------ ( 1 )
And,
From Second condition we get
= ( 1x +1y ) = 9 ( 1x×1y )
= (x + y xy) = ( 9xy)
= x + y = 9 ------- ( 2 ) ( Ans )
We can substitute value from equation 2 in equation 1 , we get
xy9 = 7
xy = 63
So our number is 63