Question

If the numerator if a certain fraction is increased by 2 and the denominator by 1, the fraction becomes equal to 5/8 and if the numerator and denominator are each diminished by 1, the fraction becomes equal to 1/2; find the fraction

Answer 1

Hiii friend,


Let the Numerator and denominator be X and Y.

Fraction = Numerator/Denominator = X/Y


According to question,

X + 2/ Y+1 = 5/8

8(X+2) = 5(Y+1)

8X + 16 = 5Y + 5

8X -5Y = 5-16

8X -5Y = -11......(1)

Again,

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


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

2X - 2 = Y - 1

2X - Y = -1+2

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


From equation (1) we get,

8X - 5Y = -11

8X = -11+5Y

X = (-11+5Y)/(8) -------(3)


Putting the value of X in equation (2)


2X - Y = 1


2 × (-11+5Y/8) -Y = 1

-11 + 5Y/4 - Y = 1

-11 + 5Y - 4Y = 4

Y = 4+11

Y = 15

Putting the value of Y in equation (3)


X = -11+5Y/8 => -11 + 5 × 15/8 = -11 + 75/8

X = 64/8 = 8


Numerator = X = 8


And,


Denominator = Y = 15.


Fraction = Numerator/Denominator = 8/15


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