Multiple choice

Mayur goes to Rajasthan by car. The entire distance is divided into 4 parts. Mayur travels with a speed of 50 km/hr for the 1st 150 km, 80 km/hr for the next 320 km, and x and y km/hr for the 3rd and 4th parts, respectively. It is given that y is 40% more than x and the time taken by Mayur to cover the 3rd part is 30 minutes less than that taken to cover the 4th part. Which of the following is true if the total distance is 900 km and the total time is 10.5 hours, where 'a' denotes the distance of the 3rd part and b denotes the distance of the 4th part?

  1. 2a = 24.5x - 2150

  2. 2a + 2150 = 23.5x

  3. 2a - 2150 = 22.5x

  4. 2a + 1150 = 25x

  5. None of these
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A Correct answer
Explanation

Total distance = 900. 1st part = 150, 2nd = 320. 3rd (a) + 4th (b) = 900 - 470 = 430. Time = 150/50 + 320/80 + a/x + b/y = 10.5. 3 + 4 + a/x + b/y = 10.5, so a/x + b/y = 3.5. Given y = 1.4x, a/x + b/(1.4x) = 3.5. Multiply by 1.4x: 1.4a + b = 4.9x. Since b = 430 - a, 1.4a + 430 - a = 4.9x, so 0.4a + 430 = 4.9x. Multiply by 5: 2a + 2150 = 24.5x. This matches option A (2a = 24.5x - 2150).

AI explanation

From the total distance of 900 km, the distance left for the third and fourth parts is 900 minus 150 minus 320, which equals 430 km; so the distance of the third part a plus the distance of the fourth part b equals 430. The total time of 10.5 hours gives the equation 150 divided by 50 plus 320 divided by 80 plus a divided by x plus b divided by y equals 10.5, which simplifies to a divided by x plus b divided by y equals 5. Since y is 40 percent more than x, y equals 1.4x; because the time for the third part is 30 minutes less than the fourth, a divided by x equals b divided by 1.4x minus 0.5. Substituting 430 minus a for b and 1.4x for y in the time equation and then substituting the relationship from the time difference gives the equation 2a equals 24.5x minus 2150.

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