Mini and Vinay are quiz masters preparing for a quiz. In x minutes,mini makes y questions more than Vinay . If it were possible to reduce the time needed by each to make a question by two minutes, then in x minutes mini would make 2y questions more than vinay. How many questions does mini make in x minute?????

Answer:- 1/4 [2(x+y) - sqrt( 2 x^2 + 4 y^2) ]

• In x minutes mini makes a questions.
  i.e.Mini makes a question in x/a minutes.
  In x minutes vinay makes a-y questions.
  Vinay makes a question in x/(a-y) minutes
  if mini makes a question in x/a-2 minutes (is equal to (x-2a)/a )and vinay makes a question in x/(a-y)-2 minutes is equal to ((x-2a+2y)/(a-y))than in x minutes mini makes 2y questions more.
  That is to say problem wants a in this equation
  ax/(x-2a)-(a-y).x/(x-2a+2y)=2y
  ax/(x-2a)-2y=(a-y).x/(x-2a+2y)
  (ax-2yx+4ay)/(x-2a)=(ax-yx)/(x-2a+2y)
  (ax-2yx+4ay).(x-2a+2y)-(x-2a)(ax-yx)=0
  (x-2a)(ax-2yx+4ay-ax+yx)+2y(ax-2yx+4ay)=0
  (x-2a)(4ay-yx)+2y(ax-2yx+4ay)=0
  (x-2a).y.(4a-x)+2y.(ax-2yx+4ay)=0
  (4ax-x^2-8a^2+2ax).y+y.(2ax-4yx+8ay)=0
  y(8ax-x^2-8a^2+8ay)=0
  y(8a(x-a+y)-x^2)=0
  8ay(x+y-a)=yx^2
  a(x+y-a)=yx^2/8y
  a(x+y-a)=x^2/8
  a^2-ax-ay+x^2/8=0
  a^2-a(x+y)+x^2/8=0
  solving for a for 2nd degree equations. (b^2-4ac formula)
  a1=((x+y)+sqrt((x+y)^2-4.x^2/8))/2 or
  a2=((x+y)-sqrt((x+y)^2-4.x^2/8))/2
• 7 years agoHelpfull: Yes(0) No(2)