Question

a fraction becomes 4/5,if 1 is added to both the neomerator and denominator.if 5 is subtracted from the neomreator and denominator,it becomes 1/2,find the fraction

Answer 1

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Answer 2

Heya !!!


Let the Numerator and denominator of a fraction be X and Y.


Fraction = Numerator/Denominator = X/Y


One is added to Numerator and Denominator then the Numerator and denominator becomes X+1 and Y+1 .


Fraction = Numerator/Denominator = X+1/Y+1.



According to question,

X+1/Y+1 = 4/5



5(X+1) = 4(Y+1)


5X + 5 = 4Y +4


5X - 4Y = 4-5


5X - 4Y = -1 -------------EQUATION (1)


Again,


5 is subtracted from numerator and Denominator then the numerator a d denominator becomes (X-5) and (Y-5) .


Fraction = Numerator/Denominator = X-5/Y-5



According to question,


X-5/Y-5 = 1/2


2(X-5) = 1(Y-5)


2X - 10 = Y -5


2X - Y = -5 +10

2X - Y = 5 -------------(2)


From equation (1) we get,


5X - 4Y = -1


5X = -1+4Y


X = -1 + 4Y/5 -----------(3)



Putting the value of X in equation (2)


2X - Y = 5


2 × (-1+4Y/5) - Y = 5


-2 + 8Y/5 - Y = 5



-2+8Y - 5Y/5 = 5


3Y -2 = 5 × 5


3Y = 25+2


3Y = 27


Y = 27/3 => 9


Putting the value of Y in equation (3)


X = -1+4Y/5 => -1 + 4 × 9/5 = -1 + 36/5


X = 35/5 => 7

Numerator = X = 7


and,


Denominator = Y = 9


Fraction = Numerator/Denominator = 7/9



HOPE IT WILL HELP YOU.... :-)