EPFO EO/AO 2023 General Ability Test · Question 101 of 120

Correct — A, (a) 108. Two trains moving towards each other on parallel tracks cross when the front of one reaches the rear of the other, so the distance covered relative to each other is the sum of the two lengths: 400 + 300 = 700 m. Because the trains travel in opposite directions, the speed at which that gap closes is the sum of the two speeds. The whole 700 m is covered in 15 seconds, so the relative speed is 700 / 15 m per second, which is 46 and two-thirds m per second. Converting to km per hour by multiplying by 18/5 gives (700 / 15) x (18 / 5) = 168 km per hour. That 168 is the sum of the two speeds, and one of them is given as 60, so the longer train runs at 168 - 60 = 108 km per hour. The same working is shorter if you never leave km per hour. The relative distance is 700 m = 0.7 km and the time is 15 seconds = 15/3600 hour = 1/240 hour, so the relative speed is 0.7 x 240 = 168 km per hour, and the answer follows in one subtraction. A candidate who prefers to work in m per second must remember to convert the given 60 km per hour as well: 60 x 5/18 = 16 and two-thirds m per second, and 46 and two-thirds - 16 and two-thirds = 30 m per second, which is 30 x 18/5 = 108 km per hour. Same answer, one more conversion. The check that settles it is to put the answer back into the question. At 108 km per hour and 60 km per hour the trains approach at 168 km per hour = 46.67 m per second, and 700 / 46.67 = 15 seconds exactly, which is what the stem says. None of the other three values reproduces 15 seconds.

• (b)102 — Put 102 back into the stem and it does not fit. The trains would approach at 102 + 60 = 162 km per hour, which is 45 m per second, and closing a 700 m gap at 45 m per second takes 700 / 45 = 15.6 seconds, not the 15 seconds the question states. This option, like (c), is placed close to the true value so that a candidate who has rounded 700 / 15 to '47 m per second' or has used 3.6 loosely as the conversion factor can land near it and feel confirmed. The defence is to keep the arithmetic exact: 700 / 15 is 140 / 3, and (140 / 3) x (18 / 5) is exactly 168, with no rounding anywhere.
• (c)98 — At 98 km per hour the approach speed would be 98 + 60 = 158 km per hour, or 43.89 m per second, and the crossing would take 700 / 43.89 = 15.95 seconds, close to 16 rather than the 15 given. Nothing in the standard relations produces 98: the sum of lengths is fixed at 700 m and the time at 15 s, so the relative speed is pinned at 168 km per hour and only one option can survive the subtraction. Notice also that the question asks for the speed of the longer train, so the 60 must be subtracted from the relative speed and not added to it; adding gives 228, which is not offered, and the absence of that value from the option set is a quiet hint that the subtraction is the intended step.
• (d)96 — This is the designed trap, and it is worth seeing exactly how it is built. If you forget that the second train has a length of its own and take the crossing as covering only the 400 m of the longer train, you get 400 / 15 = 26.67 m per second, which converts to exactly 96 km per hour. The round number feels like a confirmation, but it is the relative speed of a wrong model, and it has not even had the other train's 60 km per hour taken out of it. Two separate errors have to line up to reach it. The rule to hold is that a train crossing a pole or a man covers its own length, a train crossing a platform, a bridge or another train covers the sum of the two lengths, and only the first of those is a single-length problem.

Every train problem is one relation, distance = speed x time, applied to a carefully chosen relative distance and a relative speed. The relative distance is the length that must pass a fixed reference point on the other body before the crossing is complete: a train passing a pole, a man or any point object covers its own length; a train passing a platform, a bridge, a tunnel or another train covers the sum of the two lengths. The relative speed depends on direction: bodies moving in opposite directions close the gap at the sum of their speeds, while bodies moving in the same direction close it at the difference. Unit conversion is the third leg. To go from km per hour to m per second multiply by 5/18; to go the other way multiply by 18/5. Because examiners set the numbers so that the intended route gives a whole number, an ugly decimal in the middle of the working is usually a signal that the model, not the arithmetic, has gone wrong. The habit that makes this family reliable is to write down three quantities before touching a calculator: the relative distance in metres, the time in seconds, and the direction, and only then decide whether the two speeds are to be added or subtracted.

Quantitative aptitude occupies fixed blocks of the EO/AO General Ability Test, and speed-distance-time is one of the topics that recurs across them, because it can be tested in a single sentence and still separates candidates who have a method from candidates who improvise. With about a minute available per question, the winning approach is a two-line solution rather than a full algebraic set-up: identify the relative distance, identify the relative speed, divide. The habit rewarded here is substituting the chosen option back into the stem, which takes ten seconds and catches every one of the three wrong values on this item.

• Two trains crossing each other cover a relative distance equal to the sum of their lengths.
• Opposite directions: relative speed is the sum of the speeds. Same direction: relative speed is the difference.
• km per hour to m per second: multiply by 5/18. m per second to km per hour: multiply by 18/5.
• A train crossing a pole, a post or a standing man covers only its own length.
• A train crossing a platform or a bridge covers its own length plus the length of the platform or bridge.
• Here: (400 + 300) / 15 = 46.67 m per second = 168 km per hour of relative speed, so 168 - 60 = 108 km per hour.
• Checking backwards: 700 m at 168 km per hour takes exactly 15 seconds, which no other option reproduces.

• Using only one train's length when two bodies of finite length cross each other.
• Adding speeds for same-direction motion or subtracting them for opposite-direction motion.
• Mixing units, for example dividing metres by seconds and then comparing the result with a figure in km per hour.
• Reporting the relative speed as the answer instead of subtracting the known train's speed from it.
• Rounding 700 / 15 early; the exact fraction 140/3 converts cleanly and the decimal does not.

EO/AO papers set this family in three recurring shapes. The first gives both lengths and a time and asks for one speed, as here. The second gives speeds and lengths and asks for the crossing time, which is the same relation rearranged. The third gives a train crossing a pole and then a platform, from which both the train's length and its speed can be recovered by solving two equations. Learn the three sentences about relative distance, learn the two conversion factors, and the whole family becomes a minute a question.

No directly related past PYQ was found.

• practice — not a real PYQ

  A train 240 m long crosses a platform 180 m long in 21 seconds. What is the speed of the train in km per hour ?

  • (a)60
  • (b)66
  • (c)72
  • (d)78

  Answer(c) 72

• practice — not a real PYQ

  Two trains, 150 m and 250 m long, run on parallel tracks in the same direction at 72 km per hour and 54 km per hour respectively. How long does the faster train take to overtake the slower one completely ?

  • (a)40 seconds
  • (b)60 seconds
  • (c)80 seconds
  • (d)100 seconds

  Answer(c) 80 seconds