Maths-
General
Easy

Question

If the denominator of a certain fraction increased by 1 and the numerator by 2.The fraction becomes equal to 5/8 and if the numerator and denominator are diminished by 1, the fraction becomes equal to 1⁄2. Find the fraction.

Hint:

let the  numerator of fraction be x and denominator of fraction is y
Given, If the denominator of a certain fraction increased by 1 and the numerator by 2
The fraction becomes 5/8.
If the numerator and denominator are diminished by 1, the fraction becomes equal to 1/2.

The correct answer is: 8/15


    Ans :- 8/15 is the value of fraction .
    Explanation :-
    Step 1:- Frame the equation based on given conditions.
    let the  numerator of fraction be x and denominator of fraction is y
    Given, If the denominator of a certain fraction increased by 1 and the numerator by 2
    The fraction becomes 5/8.
    We get fraction numerator x plus 2 over denominator y plus 1 end fraction equals 5 over 8 not stretchy rightwards double arrow 8 left parenthesis x plus 2 right parenthesis equals 5 left parenthesis y plus 1 right parenthesis not stretchy rightwards double arrow 8 x plus 16 equals 5 y plus 5
    not stretchy rightwards double arrow 8 x plus 11 equals 5 y — Eq1
    If the numerator and denominator are diminished by 1, the fraction becomes equal to 1/2.
    We get fraction numerator x minus 1 over denominator y minus 1 end fraction equals 1 half not stretchy rightwards double arrow 2 left parenthesis x minus 1 right parenthesis equals left parenthesis y minus 1 right parenthesis not stretchy rightwards double arrow 2 x minus 2 equals y minus 1
    not stretchy rightwards double arrow 2 x minus 1 equals y— Eq2
    Step 2:- eliminate the y and find x
    Doing Eq1-5(Eq2) to eliminate y .
    8 x plus 11 minus 5 left parenthesis 2 x minus 1 right parenthesis equals 5 y minus 5 left parenthesis y right parenthesis not stretchy rightwards double arrow 8 x minus 10 x plus 11 plus 5 equals 0
    not stretchy rightwards double arrow 2 x equals 16
    ∴x = 8
    Step 3:- find y by substituting the value of x in eq2.
    2 x minus 3 equals y not stretchy rightwards double arrow 2 left parenthesis 8 right parenthesis minus 1 equals y
    not stretchy rightwards double arrow y equals 16 minus 1
    ∴y = 15
    We know the fraction is x/y = 8 over 15

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