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 takes 3 hr more if he decreases his speed by 40 km/hr. If the total distance was 240 km, what was his actual speed?

  1. 80 km/hr

  2. 100 km/hr

  3. 120 km/hr

  4. 75 km/hr

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

Let speed be v. Time taken = 240/v. If speed is v-40, time is 240/(v-40). The difference is 240/(v-40) - 240/v = 3. Solving 240v - 240(v-40) = 3v(v-40) leads to 9600 = 3v^2 - 120v, or v^2 - 40v - 3200 = 0. Factoring gives (v-80)(v+40)=0, so v=80.

Multiple choice

A person has to board a train from the railway station at 9:30 am. He leaves for the station from his home by car at 8 am at a speed of 40 km/hr. At about 8:15 am, he realises that, he had forgotten his reserved train ticket at home. At what speed shall he drive his car so that after taking his ticket from home, he can reach the station on time? The distance between railway station and his house is 60 km.

  1. 40 km/hr

  2. 48 km/hr

  3. 56 km/hr

  4. 60 km/hr

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

Two trains, A and B, started at the same time from Austin with speeds of 60 miles per hour and 80 miles per hour, respectively. They did not stop anywhere up to Houston. Train A reached Houston 40 minutes after train B. Find the distance between Austin and Houston.

  1. 120 miles

  2. 140 miles

  3. 160 miles

  4. 180 miles

  5. 200 miles
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let distance be D. Time for A = D/60, time for B = D/80. Difference is 40 minutes = 2/3 hours. D/60 - D/80 = 2/3. Multiplying by 240: 4D - 3D = 160. D = 160 miles.

Multiple choice

The total time taken by a boat to travel 55 km upstream and return to the starting point is 16 hours. If the speed of the stream is 3 km/hr, then what is the speed of the boat in still water?

  1. 6 km/hr

  2. 7 km/hr

  3. 8 km/hr

  4. 8.5 km/hr

  5. 9 km/hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let v be the speed of the boat. Upstream speed = v - 3, downstream speed = v + 3. Time equation: 55/(v-3) + 55/(v+3) = 16. Solving 55(v+3 + v-3) / (v^2 - 9) = 16 gives 110v = 16(v^2 - 9). 16v^2 - 110v - 144 = 0. Dividing by 2: 8v^2 - 55v - 72 = 0. Factoring gives (v - 8)(8v + 9) = 0, so v = 8.

Multiple choice

A boatman takes his boat in a river against the stream from A to B, where AB = 21 km, and again returns to A. He takes 10 hours in all. The time taken by him to cover 7 km going downstream is equal to the time taken by him to cover 3 km going against the stream. Find the velocity of the river.

  1. 2 kmph

  2. 5 kmph

  3. 3 kmph

  4. 7 kmph

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

Let v be the boat speed and u be the river speed. Time downstream for 7 km is 7/(v+u), time upstream for 3 km is 3/(v-u). Given 7/(v+u) = 3/(v-u), we get 7v-7u = 3v+3u, so 4v = 10u or v = 2.5u. Total time 21/(v-u) + 21/(v+u) = 10. Substituting v=2.5u: 21/(1.5u) + 21/(3.5u) = 10. 14/u + 6/u = 10, so 20/u = 10, u = 2.

Multiple choice

Car A starts from M and car B starts from N at the same time. M and N are 64 km apart. When they move in the same direction, they meet in 8 hours and when they move in opposite directions, they meet in 4 hours. What are the speeds of the cars?

  1. A - 10 km/hr, B - 6 km/hr

  2. A - 12 km/hr, B - 4 km/hr

  3. A - 14 km/hr, B - 14 km/hr

  4. A - 16 km/hr, B - 10 km/hr

  5. A - 20 km/hr, B - 16 km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let speeds be u and v. Relative speed in same direction is u - v = 64/8 = 8. Relative speed in opposite direction is u + v = 64/4 = 16. Solving u - v = 8 and u + v = 16 gives 2u = 24, so u = 12, and v = 4.

Multiple choice

Abraham and Lola are participating in a car race. Abraham takes 2 seconds more than Lola. If Abraham doubles his speed, he will take 1 second less than Lola. Find Abraham's speed, if the distance to be covered is 30 metres.

  1. 6 m/sec

  2. 5 m/sec

  3. 4 m/sec

  4. 3 m/sec

  5. 2 m/sec
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Abraham's speed be v and Lola's time be t. Abraham's time = 30/v = t + 2. If speed is 2v, time = 30/(2v) = 15/v = t - 1. Subtracting equations: (30/v) - (15/v) = 3, so 15/v = 3, v = 5 m/sec.