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

$A$ ship is moving in the westward direction with a speed of $10\ kmph$ and a ship $B\ 100km$ south of $A$, is moving northward with a speed oh $10\ kmph$. The time after which the distance between them becomes shortest, is
  1. $15\ h$
  2. $5\surd {2}\ h$
  3. $10\surd {2}\ h$
  4. $5\ h$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

After t hours, the horizontal separation is 10t and the vertical separation is 100 - 10t. The squared distance is (10t)^2 + (100 - 10t)^2, which is minimized when t = 5 hours.

Multiple choice

A swimmer can swim with velocity a in still water. He jumps in a river flowing with speed b. The swimmer goes a distance d downstream and then returns to original position. The time consumed in the process will be
  1. $\dfrac{3ad}{a^{2}-b^{2}}$
  2. $\dfrac{2ad}{a^{2}-b^{2}}$
  3. $\dfrac{ad}{a^{2}-b^{2}}$
  4. $\dfrac{4ad}{3a^{2}-b^{2}}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Time downstream = d / (a+b). Time upstream = d / (a-b). Total time = d/(a+b) + d/(a-b) = [d(a-b) + d(a+b)] / (a^2 - b^2) = 2ad / (a^2 - b^2).

Multiple choice

During the shooting of a super hit film 'MARD' Amitabh Bachchan was waiting for his beloved 'Amrita Singh' with his dog. When he saw her approaching, the dog was excited and dashed to her then back to master and so on, never stopping. How far would you estimate the dog ran if its speed is $30$ km/hr and each of them walked at $4$ km/hr, starting from a distance $400$m apart?
  1. $400$ m
  2. $880$ m
  3. $1500$ m
  4. $30$ km
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The dog runs at a constant speed of 30 km/hr for the entire duration that the two people are walking toward each other. The time taken for them to meet is distance / relative speed = 0.4 km / (4 + 4) km/hr = 0.05 hours. The distance the dog runs is speed * time = 30 km/hr * 0.05 hr = 1.5 km, which is 1500 m.

Multiple choice

Point $A$ and $B$ are $70\ km$ apart on a highway. A car starts from $A$ and another car starts from $B$ at the same time. If they travel in the same direction, they meet in $7$ hours, but if they travel towards each other they meet in one hour. What are their speeds?
  1. $30\ km/hr$ and $40\ km/hr$
  2. $36\ km/hr$ and $40\ km/hr$
  3. $19\ km/hr$ and $20\ km/hr$
  4. $40\ km/hr$ and $50\ km/hr$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let speeds be x and y. Same direction: 7(x-y) = 70 => x-y = 10. Opposite direction: 1(x+y) = 70 => x+y = 70. Adding equations: 2x = 80 => x = 40. Then y = 30.

Multiple choice

A bus travels at a speed of $50km/h$ to go from its origin to its destination at a distance of $300km$ and travels at a speed of $60km/h$ to return to the origin. What is the average speed of the bus?
  1. $54.55km/h$
  2. $55km/h$
  3. $55.55km/h$
  4. $54km/h$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Average speed = Total distance / Total time. Total distance = 300 + 300 = 600 km. Time 1 = 300/50 = 6 hours. Time 2 = 300/60 = 5 hours. Average speed = 600 / 11 = 54.5454... km/h.

Multiple choice

A man is driving a car at a speed of 72 kmph towards a hill. He sounds the horn and hears its echo after 2 seconds. At what distance from the hill the horn was sounded. (Velocity of sound = 340 m/s)

  1. 340 m

  2. 360 m

  3. 420 m

  4. 390 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Speed of car = 72 kmph = 20 m/s. In 2 seconds, the car travels 40m. Sound travels 340 * 2 = 680m. Total distance covered by sound = 2 * distance_to_hill - distance_car_traveled. 680 = 2d - 40, so 2d = 720, d = 360m.