Practice MCQ Questions and Answer on Speed Time and Distance
31.
A runs twice as fast as B and B runs thrice as fast as C. The distance covered by C in 72 minutes, will be covered by A in:
(A) 18 minutes
(B) 24 minutes
(C) 16 minutes
(D) 12 minutes
Solution:
Ratio of the speed of A, B and C = 6 : 3 : 1 Then, ratio of time taken; = $$\frac{{1}}{{6}}$$ : $$\frac{{1}}{{3}}$$ : 1 = 1 : 2 : 6 Hence, time taken by A = $$\frac{{72}}{{6}}$$ = 12 minutes.
32.
A man travels 210 km with the speed of 60 km/hr and next 198 km with the speed of 66 km/hr. Find the average speed of the whole journey.
Rani goes to school from her house in 30 minutes. Raja takes 45 minutes in covering the same distance. Find the ratio between time taken by Rani and Raja ?
(A) 2 : 3
(B) 4 : 3
(C) 3 : 2
(D) 1 : 3
Solution:
Rani goes to school from her house = 30 minutes Raja goes to school from his house = 45 minutes Required ratio : = 30 : 45 = 2 : 3
34.
A student walks from his house at a speed of $$2\frac{1}{2}$$ km per hour and reaches his school 6 minutes late. The next day he increases his speed by 1 km per hours and reaches 6 minutes before school time. How far is the school from his house ?
(A) $$\frac{5}{4}$$ km
(B) $$\frac{7}{4}$$ km
(C) $$\frac{9}{4}$$ km
(D) $$\frac{11}{4}$$ km
Solution:
Difference between his reaching time : = (14 - 10) hrs = 4 hrs = 4 hrs → 6m + 6m (late + before) = 4 hrs → 12 minutes = 1 unit = $$\frac{12}{4 × 60}$$ km ($$\because $$ 1 m = 60 seconds) 1 unit = $$\frac{1}{20}$$ km Then, 35 units : = 35 × $$\frac{1}{20}$$ km = $$\frac{7}{4}$$ km Then the distance between his house and school is = $$\frac{7}{4}$$ km
35.
A runs twice as fast as B and B runs thrice as fast as C. The distance covered by C in 72 minutes, will be covered by A in:
(A) 18 minutes
(B) 24 minutes
(C) 16 minutes
(D) 12 minutes
Solution:
Ratio of the speed of A, B and C = 6 : 3 : 1 Then, ratio of time taken; = $$\frac{{1}}{{6}}$$ : $$\frac{{1}}{{3}}$$ : 1 = 1 : 2 : 6 Hence, time taken by A = $$\frac{{72}}{{6}}$$ = 12 minutes.
36.
A train is scheduled to cover the distance between two stations 46 km apart in one hour. If it travels 25 km at a speed of 40 km/hr, find the speed for the remaining journey to complete it in the scheduled time :
A motorboat in still water travels at speed of 36 kmph. It goes 56 km upstream in 1 hour 45 minutes. The time taken by it to cover the same distance down the stream will be:
(A) 2 Hours 25 Minutes
(B) 3 Hours
(C) 1 Hours 24 Minutes
(D) 2 Hours 21 Minutes
Solution:
1 hour 45 minutes = $$1 + \frac{{45}}{{60}}$$ = $$\frac{7}{4}$$ hours. Speed of the motorboat up-stream, $$\eqalign{ & = \frac{{{\text{Distance}}}}{{{\text{Time}}\,\,{\text{Taken}}}} \cr & = \frac{{56\,{\text{km}}}}{{\frac{7}{4}{\text{hours}}}} \cr & = \frac{{56 \times 4}}{7} \cr & = 32\,{\text{kmph}} \cr} $$ Let the speed of the current = x kmph Hence, 36 - x = 32 Or, x = 36 - 32 = 4 kmph Speed of boat down the stream = 36 + 4 = 40 kmph. ∴ Time taken to cover 56 km at 40 kmph = $$\frac{{56}}{{40}}$$ = $$\frac{7}{5}$$ hours or 1 hours 24 minutes.
38.
Two cars start simultaneously from cities A and B, towards B and A respectively, on the same route. Once the two cars reach their destinations they turned around and move towards the other city without any loss of time. The two cars continue shuttling in this manner for exactly 20 hours. If the speed of the car starting from A is 60km/hr and the speed of the car starting from B is 40km/hr and the distance between the two cities is 120 km, find the number of times the two cars cross each other?
(A) 8
(B) 10
(C) 12
(D) 20
Solution:
Suppose both moves with the same speed 60 km/h then they will meet max 10 times. So answer will be less than 10. Thus correct answer will be 8.
39.
The area of square park is 25 sq. Km. Time taken to complete a round of the field once, at a speed of 3 kmph is:
(A) 4 hours 60 minutes
(B) 4 hours 50 minutes
(C) 6 hours 40 minutes
(D) 5 hours 40 minutes
Solution:
Area of square = side × side= 25 sq. km. Side = 5 km. perimeter = 4 × 5 = 20 km. Time taken to complete one round with speed 3 kmph, = $$\frac{{20}}{3}$$ = 6.66 hours = 6 hour 40 minutes
40.
A train passes two persons walking in the same direction at a speed of 3 kmph and 5 kmph respectively in 10 seconds and 11 seconds respectively. The speed of the train is
(A) 28 kmph
(B) 27 kmph
(C) 25 kmph
(D) 24 kmph
Solution:
1st method: Let the speed of the train be S. And length of the train be x. When a train crosses a man, its travels its own distance. $$\eqalign{ & {\text{According to question}}; \cr & \frac{x}{{ {\left( {s - 3} \right) \times {\frac{5}{{18}}} } }} = 10 \cr & {\text{or}},\,18x = 50 \times s - 150.....({\text{i}}) \cr & {\text{and}} \cr & \frac{x}{{ {\left( {x - 5} \right) \times {\frac{5}{{18}}} } }} = 11 \cr & 18x = 55 \times s - 275......({\text{ii}}) \cr & {\text{Equating equation }}\left( {\text{i}} \right){\text{ and }}\left( {{\text{ii}}} \right) \cr & 50 \times s - 150 = 55 \times s - 275 \cr & {\text{or}},\,5 \times s = 125 \cr & {\text{or}},\,s = 25\,{\text{kmph}} \cr} $$