Question

A motor boat of a fraction is 3 less than its denominator . if 2 is added to both the numerator and the denominator then the sum of the new fraction and the original fraction is 29/20

Answer 1

Let the denominator be x             Numerator  is x-3 The fraction is (x-3)/x when 2 is added to numerator and denominator         we have fraction as (x-1)/(x+2)   ATQ  (x-3)/x +(x-1)/(x+2)= 29/20    ⇒    (x-3)((x+2) +x(x-1)=x(x+2)*29/20    ⇒    (x²-6-x + x²-x)20= 29x²+58x    ⇒    40x²-120-40x=29x²+58x    ⇒    11x²-98x- 120=0    ⇒    11x² - 110x +12x -120=0    ⇒     (11x+12)(x-10)=0 Canceling the negative fraction value  of x we have x=10 Then the fraction (x-3)/x=7/10  #hope it helps..