Multiple choice

A cyclist, when increases his speed by 5 kmph, takes 2 hours less to cover 200 km. What was his original speed?

  1. 40 kmph

  2. 30 kmph

  3. 25 kmph

  4. 20 kmph

  5. 15 kmph
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let original speed be v. 200/v - 200/(v+5) = 2. 100/v - 100/(v+5) = 1. 100(v+5 - v) = v(v+5). 500 = v^2 + 5v. v^2 + 5v - 500 = 0. (v+25)(v-20) = 0. v = 20 kmph.

AI explanation

Let the original speed be v kmph, so the time taken originally is 200/v hours. When the speed increases by 5 kmph, the new time is 200/(v+5) hours, leading to the equation 200/v - 200/(v+5) = 2. Solving the equation 200(v+5-v) = 2v(v+5) gives v^2 + 5v - 500 = 0, which factors to (v+25)(v-20)=0. Discarding the negative value, the original speed is 20 kmph.

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