Multiple choice

While covering the distance of 540 km, if the speed of Car is increased by 3 kmph then it takes 2 hours less to cover the same distance then find the new speed of the car?

  1. 30 kmph

  2. 40 kmph

  3. 50 kmph

  4. 60 kmph

  5. None of these
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A Correct answer
Explanation

Let speed be v. 540/v - 540/(v+3) = 2. 540(v+3-v) / (v(v+3)) = 2. 540 * 3 = 2(v^2 + 3v). 810 = v^2 + 3v. v^2 + 3v - 810 = 0. (v+30)(v-27) = 0. v = 27. New speed = v+3 = 30.

AI explanation

Using the formula Time = Distance / Speed, the original time is 540 / x and the new time is 540 / (x + 3). The difference in time is 2 hours, so 540 / x - 540 / (x + 3) = 2. Solving the equation 540(x + 3) - 540x = 2x(x + 3) gives 1620 = 2x^2 + 6x, which simplifies to x^2 + 3x - 810 = 0. Factoring this quadratic equation yields x = 27 kmph, so the new speed of the car is 27 + 3 = 30 kmph.

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