Quantitative Aptitude

Time, Speed and Distance

2,165 Questions
All Core formulas and unit conversion 441 Boats and streams effective speed 396 Relative speed, meetings, and overtaking 375 Average speed 362 Early and late arrival 321 Proportional relationships 202 Stoppage time per hour 35 Train and stationary or moving object crossing 17 Races and dead heats 16

Time, Speed and Distance Questions

Multiple choice

A boy is running at a speed of $p$ km/hr to cover a distance of $1$ km. But, due to slippery ground, his speed is reduced by $q$ km/hr $(p > q).$ If he takes $r$ hours to cover the distance, then,
  1. $\displaystyle \frac{1}{r} = (p - q)$
  2. $r = (p - q)$
  3. $\displaystyle \frac{1}{r} = (p + q)$
  4. $r = (p + q)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Time = Distance / Speed. The distance is 1 km. The reduced speed is (p - q) km/hr. The time taken is r hours. Therefore, r = 1 / (p - q), which implies 1/r = p - q.

Multiple choice

A star is $8.1 \times 10^{13} km$ away from the earth. Suppose right travels at the speed of $3.0 \times 10^5 km$ per second, how long will it take light from the star to reach the earth?
  1. $7.5 \times 10^3 hrs$
  2. $7.5 \times 10^4 hrs$
  3. $2.5 \times 10^{10} sec$
  4. $2.7 \times 10^{11} sec$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Time = Distance / Speed = (8.1 * 10^13) / (3.0 * 10^5) = 2.7 * 10^8 seconds. Convert to hours: (2.7 * 10^8) / 3600 = 2.7 * 10^8 / (3.6 * 10^3) = 0.75 * 10^5 = 7.5 * 10^4 hours.

Multiple choice

If a train runs at $40$ km/hr, it reaches its destination late by $11$ minutes, but if it runs at $50$ km/hr, it is late by $5$ minutes only. The correct time for the train to complete the journey is
  1. $13$ min
  2. $15$ min
  3. $19$ min
  4. $21$ min
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let distance be D and time be T. D/40 = T + 11/60 and D/50 = T + 5/60. Subtracting: D/40 - D/50 = 6/60 = 1/10. D/200 = 1/10 => D = 20 km. Time taken at 40 km/h = 20/40 = 0.5 hours = 30 min. Since it is 11 min late, the correct time is 30 - 11 = 19 min.

Multiple choice

Starting from his house one day, a student walks at a speed of $\displaystyle 2\dfrac {1}{2}$ km/hour and reaches his school $6$ minutes late. Next day he increased his speed by $1$ km/hr and reaches the school $6$ minutes early. How far is the school from his house?
  1. $1$ km
  2. $1 \displaystyle \dfrac {1}{2}$ km
  3. $1 \displaystyle \dfrac {3}{4}$ km
  4. $2$ km
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let d be the distance. Time taken at 2.5 km/hr is d/2.5, and at 3.5 km/hr is d/3.5. The difference in time is 12 minutes (0.2 hours). Solving d/2.5 - d/3.5 = 0.2 leads to d = 1.75 km.

Multiple choice

A motor starts with the speed of 70 km/hr with its speed increasing every two hours by 10 km/hr. In how many hours will it cover 345 km?
  1. $\displaystyle 2\frac {1}{4}$ h
  2. $\displaystyle 4\frac {1}{2}$ h
  3. $4 h \ 5 min$

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Hours 1-2: 70 km/hr * 2 = 140 km. Hours 3-4: 80 km/hr * 2 = 160 km. Total = 300 km. Remaining = 45 km. Speed for next interval = 90 km/hr. Time = 45/90 = 0.5 hours. Total time = 2 + 2 + 0.5 = 4.5 hours.

Multiple choice

An aircraft was to take off from a certain airport at 8 am but it was delayed by 30 min To make up for the lost time it was to increase its speed by 250 km/hr from the normal speed to reach its destination 1500 km on time What was the normal speed of the aircraft?

  1. 650 km/hr

  2. 750 km/hr

  3. 850 km/hr

  4. 1000 km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let normal speed be v. Time taken = 1500/v. New time = 1500/(v+250). Difference is 0.5 hours. Solving 1500/v - 1500/(v+250) = 0.5 leads to v^2 + 250v - 750000 = 0, giving v = 750.

Multiple choice

Ram travels from P to Q at 10 km/hr and returns at 15 km/hr Shyam travels from P to Q and returns at 12.5 km/hr If he takes 12 minutes less than Ram then what is the distance between P and Q?

  1. 60 km

  2. 45 km

  3. 36 km

  4. 30 km
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let distance be D. Ram's time = D/10 + D/15 = D/6. Shyam's time = D/12.5 + D/12.5 = 2D/12.5 = D/6.25. Difference = D/6.25 - D/6 = 12/60 hours = 0.2 hours. (6D - 6.25D) / 37.5 = 0.2. 0.25D = 7.5. D = 30 km.

Multiple choice

A student reached his school late by 20 minutes by travelling at a speed of 9 km/hr Had he travelled at the speed of 12 km/hr he would have reached his school 20 minutes early Find the distance between his house and the school?

  1. 12 km

  2. 6 km

  3. 3 km

  4. 24 km
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let distance be D. Time taken at 9 km/hr is D/9 and at 12 km/hr is D/12. The difference in time is 40 minutes (20 late + 20 early), which is 2/3 hours. Solving D/9 - D/12 = 2/3 gives D/36 = 2/3, so D = 24 km.