a two digit number is such that the product of the digit is 35,when 18 is added to the number,the digits interchange their places.find the number

Asked by chandrika bhosge | 20th Oct, 2013, 07:49: AM

Expert Answer:

Consider a two digit number xy.
 
Therefore the decimal expansion is 10x + y
 
The product of their digit is 35.
 
Therefore, xy = 35
 
Thus, y = (35/x)  .....(1)
 
When 18 is added, the sum is (10x + y) + 18.
 
Given that when 18 is added to the number, the digits are interchanged.
 
When digits are interchanged, the decimal expansion of the number (yx) is 10y + x
 
Therefore, (10x + y) + 18 = 10y + x
 
9x - 9y + 18 = 0
 
x - y + 2 = 0
 
Substituting the value of y from equation (1) we have
 
x - (35/x) + 2 = 0
 

Answered by Vimala Ramamurthy | 20th Oct, 2013, 01:55: PM

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