Multiple choice

Directions: Compare Quantity I and Quantity II using additional information given above the two quantities, if such information is given, and select one of the following five answer choices. Find the distance covered. Quantity I: A truck driver covers certain distance in 12 hours. He covers first half at 32 kmph and second half at 25% increased speed than in first half. Quantity II: Two cars move toward each other at speeds of 50 kmph and 60 kmph. When both meet, it is found that the faster car covered 40 km more than the slower one.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II, or no relation can be established.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: Total distance D, time 12h. Half distance D/2 at 32 kmph, half at 32*1.25 = 40 kmph. Time = (D/2)/32 + (D/2)/40 = D/64 + D/80 = 9D/320 = 12. D = 12 * 320 / 9 = 426.67 km. Quantity II: Relative speed = 50+60 = 110. Faster car covers 40km more. Let time be t. 60t - 50t = 40, so t = 4 hours. Total distance = (50+60)*4 = 440 km. Quantity II > Quantity I.

AI explanation

For Quantity I, the second half speed is 32 kmph multiplied by 1.25, which equals 40 kmph; since each half takes 6 hours, the distance is 6 times 32 plus 6 times 40, totaling 432 km. For Quantity II, the faster car covers 40 km more than the slower one, so using their speeds of 60 kmph and 50 kmph, the time until they meet is 40 divided by (60 - 50), which equals 4 hours; the total distance is (60 + 50) multiplied by 4, equaling 440 km. Comparing the two quantities, 440 km is greater than 432 km.

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