Multiple choice

A plane left $30$ min later from the schedule time and in order to reach the destination $1500$ km on time, it had increase the speed by $250$ kmph from the usual speed, its usual speed is :-

  1. $700$ kmph
  2. $750$ kmph
  3. $250$ kmph
  4. $350$ kmph
  5. $500$ kmph
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let usual speed be v. Time = 1500/v. New time = 1500/(v+250). Difference = 0.5 hours. 1500/v - 1500/(v+250) = 0.5. Solving this quadratic gives v = 750.

AI explanation

Let the usual speed be x kmph, so the usual time is 1500/x hours and the new time is 1500/(x+250) hours. Because the plane left 30 minutes late, which is 0.5 hours, the difference in time is 0.5, giving the equation 1500/x - 1500/(x+250) = 0.5. Multiplying by 2x(x+250) yields 3000(x+250) - 3000x = x(x+250), which simplifies to x^2 + 250x - 750000 = 0. Factoring this gives (x - 750)(x + 1000) = 0, so the usual speed is 750 kmph.

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