Multiple choice

A cyclist started with a speed of 30 km/hr in a race. After every lap of one hour each, he increased his speed by 5 km/h. In how many laps will he cover 450 km?

  1. 8

  2. 9

  3. 10

  4. 11

  5. 12
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Distance covered in each hour: 30, 35, 40, 45, 50, 55, 60, 65, 70. Summing these: 30+35+40+45+50+55+60+65+70 = 450. This takes 9 hours, which is 9 laps.

AI explanation

The distances covered each lap form an arithmetic progression where the first lap is 30 km, the second is 35 km, the third is 40 km, and so on. Using the sum formula for an arithmetic progression, 450 = n/2 * (2 * 30 + (n - 1) * 5), which simplifies to the quadratic equation n^2 + 11n - 180 = 0. Factoring this gives (n - 9)(n + 20) = 0, so the positive integer is 9 laps.

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