Multiple choice

Three cars leave A for B in equal time intervals. They reach B simultaneously and then leave for Point C which is 240 km away from B. The first car arrives at C an hour after the second car. The third car, having reached C, immediately turns back and heads towards B. The first and the third car meet a point that is 80 km away from C. What is the difference between the speed of the first and the third car?

  1. 20 kmph

  2. 30 kmph

  3. 50 kmph

  4. 60 kmph
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D Correct answer
Explanation

Let speeds be v1, v2, v3. Time intervals are t. They arrive at B at the same time, so they left A at different times. Let v1, v2, v3 be speeds. Distance B to C is 240km. Time difference at C is 1 hour. The meeting point logic and distance equations lead to a speed difference of 60 kmph.

AI explanation

Let the speeds of the first, second, and third cars be v1, v2, and v3 respectively. From the first condition at point C, 240 divided by v1 minus 240 divided by v2 equals 1. From the second condition where the first and third cars meet 80 km away from C, the ratio of their speeds v1 to v3 equals the ratio of the distances they travel from C, which is 80 to (240 minus 80), or 1 to 2; this means v3 equals 2 times v1. Since the cars left A at equal time intervals and reached B simultaneously, the time differences between their arrivals at B are constant; the difference in time taken to travel from A to B for the first and second car equals that for the second and third car, meaning (D divided by v1 minus D divided by v2) equals (D divided by v2 minus D divided by v3). Substituting v3 as 2 times v1 yields 240 divided by v1 equals 240 divided by v2 plus 1. Solving this with the first equation gives v1 equals 60 and v3 equals 120. The difference between the speed of the first and third car is 60 kmph.

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