The sum of numerator and denominator of a fraction is 8 if 2 is added to the numerator and to the denominator the value of fraction increased by4÷35 find the fraction.
Answers
Solution :-
Let the numerator and denominator be x and y respectively.
Given : Sum of numerator and denominator of a fraction is 8
x + y = 8
=> x = 8 - y ______(i)
Given : 2 is added to the numerator and to the denominator the value of fraction increased by 4/35
(x + 2)/(y + 2) = x/y + 4/35 _____(ii)
Putting the value of x in equation (ii) we get,
(8 - y + 2)/(y + 2) = (8 - y)/y + 4/35
=> (10 - y)/(y + 2) = {35(8 - y) + (4y}/35y
=> 35y(10 - y) = (y + 2) (280 - 31y)
=> 350y - 35y² = 280y - 31y² + 560 - 62y
=> - 35y² + 31y² + 350y - 280y + 62y - 560 = 0
=> - 4y² + 132y - 560 = 0
=> - 4(y² - 33y + 140) = 0
=> y² - 28y - 5y + 140 = 0
=> y(y - 28) - 5(y - 28) = 0
=> (y - 28) (y - 5) = 0
=> y = 28 or y = 5
Putting the value of y in equation (i) we get,
x + 28 = 8 or x + 5 = 8
=> x = 8 - 28 or x = 8 - 5
=> x = - 20 or x = 3
Therefore,
Numerator = x = 3
Denominator = y = 5
Hence,
Fraction = 3/5