Question

The numerator of the fraction is 3 less than its denominator. If the denominator is increased by 5 and the numerator by 2 we get the fraction as find the fraction.

Answer 1

Let The Value of The Denominator = x,

& Thus, The Numerator = x +5,

Let the Value of This Fraction, (x+5)/x = y, ….(1)

We are Given A fraction with Value of Denominator Increased by 5, such that:-

(x + 5)/(x + 5)=y - 5/4,

ie. y - 5/4 =1,

ie. 4y-5/4=1,

ie. 4y - 5=4, (cross -multiplying)

ie. 4y =5+4

ie. y =9/4 ….(2)

[This is the Sought Answer & Value Of The Equation & Our Answer ]

Even at this stage, We can see that Value Of Equation Makes Denominator Value 'x' =4, & Numerator Value as 'x + 5′ =9,

However, we will show it by Substituting the Value of y in Equation (2) in Equation (1) :-

(x +5)/x = 9/4,

4x + 20 =9x, (cross- multiplying),

ie. 9x - 4x =20,

ie. 5x =20,

ie. x =4 (Ans)

& our Fraction Becomes (4+5)/4 =9/4,

Hope it Helped