A two digit number is 5 times the sum of its digits and is also equal to 5 more than twice the product of its digits.Find the number.

Asked by Archana Tikayat Ray | 16th Oct, 2010, 07:45: PM

Expert Answer:

Dear student,
 
Let the 2 digit number be 10x+y
 
given : 10x+y = 5(x+y)
          5x -4y = 0  --------(1)
 
Also 10x+y = 5+2xy
putting y = 5x/4 from equation (1)
 
10x + 5x/4 = 5 + 2x(5x/4)
(45x)/4 = 5 + (5x2 )/2
 
45x = 20 + 10x2
10x-45x +20 =0 
2x-9x +4 =0
 (x-4)(2x-1) = 0
 
hence x = 4 or 1/2
but x is an integer. so x=4
y = 5x/4= 5
 
the number is 10x + y = 40+5=45
 
We hope this clarifies your query,
regards,
Team topper learning.

Answered by  | 17th Oct, 2010, 10:45: PM

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