Time and Distance: Formulas, Shortcuts and Solved Examples — MCQs with Answers (Set 6)

Let the speeds of A and B be in the ratio 8 : 3. For a fixed distance, time is inversely proportional to speed. So the time ratio is 1/8 : 1/3, which simplifies to 3 : 8. Check: speed x time for A = 8 x 3 = 24. Speed x time for B = 3 x 8 = 24. Both give the same distance, so 3:8 is the correct time ratio.

Let the speeds of A and B be in the ratio 7 : 8. For a fixed distance, time is inversely proportional to speed. So the time ratio is 1/7 : 1/8, which simplifies to 8 : 7. Check: speed x time for A = 7 x 8 = 56. Speed x time for B = 8 x 7 = 56. Both give the same distance, so 8:7 is the correct time ratio.

Let the speeds of A and B be in the ratio 7 : 2. For a fixed distance, time is inversely proportional to speed. So the time ratio is 1/7 : 1/2, which simplifies to 2 : 7. Check: speed x time for A = 7 x 2 = 14. Speed x time for B = 2 x 7 = 14. Both give the same distance, so 2:7 is the correct time ratio.

Let the speeds of A and B be in the ratio 5 : 8. For a fixed distance, time is inversely proportional to speed. So the time ratio is 1/5 : 1/8, which simplifies to 8 : 5. Check: speed x time for A = 5 x 8 = 40. Speed x time for B = 8 x 5 = 40. Both give the same distance, so 8:5 is the correct time ratio.

Let the speeds of A and B be in the ratio 2 : 9. For a fixed distance, time is inversely proportional to speed. So the time ratio is 1/2 : 1/9, which simplifies to 9 : 2. Check: speed x time for A = 2 x 9 = 18. Speed x time for B = 9 x 2 = 18. Both give the same distance, so 9:2 is the correct time ratio.

Let distance = D = 142 km and time = T = 2 hours. Speed = D / T. Speed = 142 / 2 = 71 km/hr. Check: 71 x 2 = 142 km, which matches the given distance.

Let distance = D = 472 km and time = T = 8 hours. Speed = D / T. Speed = 472 / 8 = 59 km/hr. Check: 59 x 8 = 472 km, which matches the given distance.

Let distance = D = 352 km and time = T = 4 hours. Speed = D / T. Speed = 352 / 4 = 88 km/hr. Check: 88 x 4 = 352 km, which matches the given distance.

Let distance = D = 60 km and time = T = 2 hours. Speed = D / T. Speed = 60 / 2 = 30 km/hr. Check: 30 x 2 = 60 km, which matches the given distance.

Let distance = D = 420 km and time = T = 10 hours. Speed = D / T. Speed = 420 / 10 = 42 km/hr. Check: 42 x 10 = 420 km, which matches the given distance.

Let distance = D = 800 km and time = T = 8 hours. Speed = D / T. Speed = 800 / 8 = 100 km/hr. Check: 100 x 8 = 800 km, which matches the given distance.

Let distance = D = 584 km and time = T = 8 hours. Speed = D / T. Speed = 584 / 8 = 73 km/hr. Check: 73 x 8 = 584 km, which matches the given distance.

Let distance = D = 156 km and time = T = 4 hours. Speed = D / T. Speed = 156 / 4 = 39 km/hr. Check: 39 x 4 = 156 km, which matches the given distance.

Let distance = D = 180 km and time = T = 6 hours. Speed = D / T. Speed = 180 / 6 = 30 km/hr. Check: 30 x 6 = 180 km, which matches the given distance.

Let distance = D = 272 km and time = T = 4 hours. Speed = D / T. Speed = 272 / 4 = 68 km/hr. Check: 68 x 4 = 272 km, which matches the given distance.

Let speed = 24 km/hr and distance = 400 m. Convert speed to m/sec: 24 x 5/18 = 6.67 m/sec. Time = distance / speed. Time = 400 / 6.67 = 60 seconds. Convert seconds to minutes: 60/60 = 1 minute. Check: 1 x 60 = 60 seconds, matching the time found above.

Let speed = 24 km/hr and distance = 400 m. Convert speed to m/sec: 24 x 5/18 = 6.67 m/sec. Time = distance / speed. Time = 400 / 6.67 = 60 seconds. Convert seconds to minutes: 60/60 = 1 minute. Check: 1 x 60 = 60 seconds, matching the time found above.

Let speed = 30 km/hr and distance = 1500 m. Convert speed to m/sec: 30 x 5/18 = 8.33 m/sec. Time = distance / speed. Time = 1500 / 8.33 = 180 seconds. Convert seconds to minutes: 180/60 = 3 minutes. Check: 3 x 60 = 180 seconds, matching the time found above.

Let speed = 20 km/hr and distance = 2000 m. Convert speed to m/sec: 20 x 5/18 = 5.56 m/sec. Time = distance / speed. Time = 2000 / 5.56 = 360 seconds. Convert seconds to minutes: 360/60 = 6 minutes. Check: 6 x 60 = 360 seconds, matching the time found above.

Let speed = 24 km/hr and distance = 1200 m. Convert speed to m/sec: 24 x 5/18 = 6.67 m/sec. Time = distance / speed. Time = 1200 / 6.67 = 180 seconds. Convert seconds to minutes: 180/60 = 3 minutes. Check: 3 x 60 = 180 seconds, matching the time found above.

Let speed = 15 km/hr and distance = 2000 m. Convert speed to m/sec: 15 x 5/18 = 4.17 m/sec. Time = distance / speed. Time = 2000 / 4.17 = 480 seconds. Convert seconds to minutes: 480/60 = 8 minutes. Check: 8 x 60 = 480 seconds, matching the time found above.

Let speed = 18 km/hr and distance = 1800 m. Convert speed to m/sec: 18 x 5/18 = 5 m/sec. Time = distance / speed. Time = 1800 / 5 = 360 seconds. Convert seconds to minutes: 360/60 = 6 minutes. Check: 6 x 60 = 360 seconds, matching the time found above.

Let speed = 12 km/hr and distance = 200 m. Convert speed to m/sec: 12 x 5/18 = 3.33 m/sec. Time = distance / speed. Time = 200 / 3.33 = 60 seconds. Convert seconds to minutes: 60/60 = 1 minute. Check: 1 x 60 = 60 seconds, matching the time found above.

Let speed = 18 km/hr and distance = 300 m. Convert speed to m/sec: 18 x 5/18 = 5 m/sec. Time = distance / speed. Time = 300 / 5 = 60 seconds. Convert seconds to minutes: 60/60 = 1 minute. Check: 1 x 60 = 60 seconds, matching the time found above.

Let speed = 15 km/hr and distance = 1000 m. Convert speed to m/sec: 15 x 5/18 = 4.17 m/sec. Time = distance / speed. Time = 1000 / 4.17 = 240 seconds. Convert seconds to minutes: 240/60 = 4 minutes. Check: 4 x 60 = 240 seconds, matching the time found above.