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 man rowing at the rate of 5 km/hr in still water takes thrice as much time in going 40 km up the river as in going 40 km down the river. What is the rate of flow of the stream?

  1. 1.5 km/hr

  2. 2.5 km/hr

  3. 3.5 km/hr

  4. 4.5 km/hr

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let v be the stream speed. Upstream speed is 5-v, downstream is 5+v. Time taken upstream is 40/(5-v) and downstream is 40/(5+v). Given 40/(5-v) = 3 * 40/(5+v), so 5+v = 3(5-v), which simplifies to 5+v = 15-3v, 4v = 10, v = 2.5 km/hr.

Multiple choice

What would be the approximate average speed of a car covering a distance of 440 m, if its speed while going to a place at 220 m was 70 m/sec and while coming back was 72 m/sec?

  1. 78 m/sec

  2. 75 m/sec

  3. 71 m/sec

  4. 67 m/sec

  5. 64 m/sec
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average speed = Total distance / Total time. Total distance = 440 m. Time taken for first 220 m = 220/70 = 22/7 sec. Time taken for return 220 m = 220/72 = 55/18 sec. Total time = 22/7 + 55/18 = (396 + 385) / 126 = 781/126 sec. Average speed = 440 / (781/126) = 55440 / 781 approx 71 m/sec.

Multiple choice

A train met with an accident 120 km away from station A. It completed the remaining journey at 4/5th of the original speed and reached station B, 1 hour 12 minutes late. Had the accident taken place 60 km further, the train would have been only 1 hour late. What was the original speed of the train?

  1. 60 km/hr

  2. 55 km/hr

  3. 65 km/hr

  4. 75 km/hr

  5. 70 km/hr
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let original speed be V. Time saved by traveling 60 km at speed V instead of 0.8V is 12 minutes (0.2 hours). 60/(0.8V) - 60/V = 0.2. 75/V - 60/V = 0.2. 15/V = 0.2. V = 75 km/hr.

Multiple choice

If Anita traveled by car at 80 km/hr instead of 35 km/hr, she would have covered 25 kilometers more in the same time. So, find out the actual distance covered by Anita.

  1. 19.44 km

  2. 49.07 km

  3. 20 km

  4. 26.75 km

  5. 31.3 km
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let t be the time in hours. The distance is 80t = 35t + 25, which simplifies to 45t = 25, so t = 25/45 = 5/9 hours. The actual distance covered is 35 * (5/9) = 175/9, which is approximately 19.44 km.

Multiple choice

A and B run a 1760 m race ending in a dead heat. At first, A runs 20% faster than B. Then, B speeds up and for the remaining distance, he runs 20% faster than A. At the time B speeds up, A has already run

  1. 960 m

  2. 1000 m

  3. 790 m

  4. 990 m

  5. 880 m
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the speeds of A and B be vA and vB. Initially, vA = 1.2vB. Later, vB = 1.2vA. Since they finish at the same time, the time taken for each segment must balance. Solving the ratio of distances leads to A having run 960 m when B speeds up.

Multiple choice

A man swimming in a river, which flows at 1 1 2 km/hr, finds that in a given time, he can swim twice as far along the stream as he can against it. At what speed does he swim in still water?

  1. 5 1 2 km/hr

  2. 4 1 2 km/hr

  3. 7 1 2 km/hr

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the swimmer's speed in still water be v km/hr and the stream speed be 1.5 km/hr. Since downstream distance is twice upstream distance in the same time, (v + 1.5)/(v - 1.5) = 2, giving v = 4.5 km/hr.

Multiple choice

A man took 14 hours to row a distance of 48 km downstream and return back to the starting point. He found that he can row 4 km with the stream in the same time as 3 km against the stream. What is the speed of flow of water in the stream?

  1. 1 km/hour

  2. 2 km/hour

  3. 2.5 km/hour

  4. 3 km/hour

  5. 3.5 km/hour
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let boat speed be b and stream speed be s. Downstream speed = b+s, upstream = b-s. 48/(b+s) + 48/(b-s) = 14. Also, 4/(b+s) = 3/(b-s) implies 4(b-s) = 3(b+s), so 4b-4s = 3b+3s, b = 7s. Substituting b=7s into the time equation: 48/8s + 48/6s = 14, 6/s + 8/s = 14, 14/s = 14, s = 1.

Multiple choice

Mohan travels a certain distance with a uniform speed. If he increases his speed by 3 km per hour, then he takes 40 minutes less. If he reduces his speed by 2 km per hour, then he takes 40 minutes more. What is the normal speed of Mohan?

  1. 8 km/hour

  2. 10 km/hour

  3. 12 km/hour

  4. 13 km/hour

  5. 15 km/hour
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speed be v and distance be d. d/v - d/(v+3) = 40/60 = 2/3. d/(v-2) - d/v = 40/60 = 2/3. d(3/(v(v+3))) = 2/3 => d = 2v(v+3)/9. d(2/(v(v-2))) = 2/3 => d = v(v-2)/3. Equating: 2v(v+3)/9 = v(v-2)/3 => 2v+6 = 3v-6 => v = 12.

Multiple choice

Directions: Each of the following questions consists of a question followed by three statements I, II and Ill. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. What is the speed of a boat in still water? I. The boat covers 12 km in 2 hours downstream. II. The boat covers the same distance in 4 hours upstream. III. The speed of the stream is one-third that of the boat in still water.

  1. Both I and II

  2. I and either II or III

  3. All I, II and III

  4. Data insufficient

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement I gives the downstream speed as 6 km/h. With statement II, the upstream speed is 3 km/h, so the still-water speed is 4.5 km/h. With statement III, the stream speed is one-third of the boat speed, which also determines the still-water speed from statement I, so I and either II or III are sufficient.

Multiple choice

Two friends x and y started from city P and went to city Q, which was 240 km away. Mr. x maintained a speed of 40 kmph for a certain distance and then increased his speed to 60 kmph, whereas Mr. y started with 30 kmph and exactly at half the way through increased his speed to 80 kmph. If both x and y reached Q at the same time, then at what distance from P did Mr. x change his speed?

  1. 130 km

  2. 150 km

  3. 180 km

  4. 200 km

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total distance = 240 km. Y travels at 30 km/h for 120 km (4 hours) and 80 km/h for 120 km (1.5 hours). Total time = 5.5 hours. X travels d km at 40 km/h and (240-d) km at 60 km/h. d/40 + (240-d)/60 = 5.5. Multiply by 120: 3d + 2(240-d) = 660. 3d + 480 - 2d = 660. d = 180.