Question

A number consists of two digits.when it is divided by the sum of the digits,the quotient is 7.the sum of the reciprocals of the digits is 9times the product of the reciprocals of the digits.find the number

Answer 1

Answer:
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                   ( Ans )