Quantitative Aptitude - SPLessons

Time and Distance Practice Set 1

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Time and Distance Practice Set 1

shape Introduction

Time and distance as a topic involves a variety of areas which include speed-time-distance concepts, relative speed, moving and stationary bodies, boats and streams, circular motion, and so on. Time and Distance Practice Set 1 article is useful for candidates preparing for different competitive examinations like RRB ALP/Technical Exams/Junior Engineer Recruitment Exams, SSC, IBPS PO Exams and etc.


shape Quiz

1. A man can reach a certain place in 40 hours. If he reduces his speed by 1/15th, he goes 5 km less in that time. Find the total distance covered by him.

    A. 60 km.
    B. 85 km.
    C. 75 km.
    D. 52 km.


Answer: Option C

Explanation: Let Distance = D km, Speed = S km/h

Time = \(\frac{Distance}{Speed}\) – (1)
40 = \(\frac{Distance}{Speed}\)
After reducing speed,
Distance = Distance – 5 km, Speed = S × \(\frac{14}{15}\)km/h
Time = \(\frac{(Distance – 5)}{\frac{14}{15} ×{Speed}}\) (2)
After solving equation 1 and 2
\(\frac{Distance}{Speed}\) = \(\frac{(Distance – 5)}{\frac{14}{15} ×{Speed}}\)
14 Distance = 15 (Distance – 5)

14 Distance = 15 Distance – 75

Distance = 75 km.


2. A person travelled 132 km by auto, 852 km by train and 248 km by bike. It took 21 hours in all. If the speed of train is 6 times the speed of auto and 1.5 times speed of bike, what is the speed of train?

    A. 78 km\({h}^{-1}\)
    B. 104 km\({h}^{-1}\)
    C. 96 km\({h}^{-1}\)
    D. 88 km\({h}^{-1}\)


Answer: Option C

Explanation: Let the speed of auto be km\({h}^{-1}\) So, the speed of train will be 6x and that of bike will be
= \(\frac{6×}{1.5}\) = 4x
As per the given information, ⇒ \(\frac{132}{×}\) + \(\frac{852}{6×}\) + \(\frac{248}{4×}\) = 21

∴ × = \(\frac{336}{21}\) = 16

∴ Speed of the train = 6x = 6 × 16 = 96 km\({h}^{-1}\)


3. A car drove from Agra to Delhi without stopping. It covered the first 50 miles of its journey at an average speed of 25 mph. What was the car’s average speed (in mph), for the remaining 130 miles if its overall average speed was 45 mph?

    A. 28
    B. 40
    C. 50
    D. 65


Answer: Option D

Explanation:
Average speed =\(\frac{total distance }{total time}\)
Total distance = 50 + 130 = 180 miles

∴ Total time = \(\frac{180}{45}\)= 4 hours.
Time spent for the first 50 miles = \(\frac{50}{25}\)= 2 hours
∴ Time spent on the remaining journey = 4 − 2 = 2 hours

∴ Average speed for the remaining 130 miles = \(\frac{130}{2}\) = 65 mph


4. A motor car does a journey in 16 hours, covering the first half at 30 Km/hr and the second half at 50 Km/hr. What is the distance covered?

    A. 480 km
    B. 540 km

    C. 500 km
    D. 600 km


Answer: Option D

Explanation: Since different speeds are traveled for equal distance, the average speed can be found out

Average speed = \(\frac{2 × 30 × 50}{30 + 50}\) = \(\frac{300}{8}\) km/h
Distance covered = \(\frac{300}{8}\)× 16 = 600 km


5. A and B are two stations 1200 km apart. Train X starts from station A towards station B at 60 kmph 2 hours before train Y starts from station B towards station A. If they meet at a point 360 km from station B, What is the speed of Train Y?

    A. 45 kmph
    B. 90 kmph
    C. 60 kmph
    D. 30 kmph


Answer: Option D

Explanation: Q’s 8 days work =[ \(\frac{1}{20}\) x 8] work ⇒ \(\frac{2}{5}\)The distance covered by X in 2 hours is 2 × 60 = 120 km

The distance remaining is 1080 km

This distance travelled before meeting is directly proportional to their speed

They meet 360 km from B. Hence, train Y must’ve travelled 360 km

X has travelled 720 km and Y has travelled only 360 km in the same time

This means that speed of X is twice of Y

Since speed of X is 60 kmph therefore speed of Y is 30 kmph

1. The speeds of the Shaan and Rohan are 50 km/h and 30 km/h respectively. Initially Shaan is at a place N and Rohan is at a place M. The distance between M and N is 710 km. Shaan started his journey 3 hours earlier than Rohan to meet each other. If they meet each other at a place R somewhere between M and N. then the distance between R and N is

    A. 210 km
    B. 500 km
    C. 430 km

    D. 620 km


Answer: Option B

Explanation: Distance covered by Shaan in 3 hours = 3 × 50 = 150 km

∴ Remaining distance = 710 – 150 = 560 km Relative speed = 50 + 30 = 80 kmph

∴ They meet after = \(\frac{560}{80}\) = 7 hours

Now, Shaan covers the total distance in (7 + 3 )= 10 hours

∴ Distaance covered by Shaan in 10 hours = 50 × 10 = 500 km

∴ Distance between R and N = 500 km.


2. The distance between two places A and B is 370 km. the \({1}^{st}\) car departs from place A to B, at a speed of 80 kmph at 10 am and \({2}^{nd}\) car departs from place B to A at a speed of 50 kmph at 1 pm. At what time both cars meet each other?


    A. 2 : 30 pm
    B. 2 : 00 pm
    C. 2 : 10 pm
    D. 2 : 20 pm


Answer: Option B

Explanation: Total distance = 370 km
Now, the distance covered by first car in (10 am to 1 pm =) 3 hours = 80 × 3 = 240 km
Remaining distance = 370 – 240 = 130 km
Relative speed = 80 + 50 = 130 kmph
Now, they cover 130 km in \(\frac{130}{130 = }\)\(\frac{11}{1 }\) hours = 60 mins
So, they meet 60 mins after 1 pm. So, required answer = 2 : 00 pm


3. A man takes 5 hours 45 minutes to walk to a certain place and ride back. He would have saved 2 hours had he ridden both ways. The time he would take to walk both ways is

    A. 3 hours 45 minutes

    B. 7 hours 30 minutes

    C. 7 hours 45 minutes

    D. 11 hours 45 minutes


Answer: Option C

Explanation: 1 Bike + 1 Walk = 5 hrs 45 mins

2 Bike = 3 hrs 45 mins

Hence 1 way Bike journey takes 1 hrs 52.5 mins

So, 1 way walk should take (5 hr 45 mins) – (1 hrs 52.5 mins) = 3 hr 52.5 mins

2-way walk would take: 3 hr 52.5 mins 2 = 7 hr 45 mins


4. A and B start at the same time with speeds of 40 km/hr and 50 km/hr respectively. If in covering the journey A takes 15 minutes longer than B, the total distance of the journey is

    A. 46 km
    B. 48 km
    C. 50 km
    D. 52 km
    E. More than 6 days


Answer: Option C

Explanation: Let x be the total distance of the journey.

Time taken by A – Time taken by B = 15 minutes = \(\frac{1}{4}\) hours
= \(\frac{ ×}{40}\) – \(\frac{ ×}{50}\)= \(\frac{1}{4}\)
⇒ \(\frac{ × }{200}\)= \(\frac{1}{4}\)
∴ x = 50 km


5.A motor starts with the speed of 70 kmph with its speed increasing every two hours by 10 kmph. In how many hours will it cover 345 kms?

    A. 2\(\frac{1}{4}\) hours
    B. 4\(\frac{1}{2}\) hours
    C. 4 hours 5 minutes
    D. Can’t be determined


Answer: Option B

Explanation: Distance covered in first two hours = 70 × 2 = 140 km

Distance covered in next two hours = 80 × 2 = 160 km

Distance covered in first four hours = 140 + 160 = 300 km

Remaining distance = 345 – 300 = 45 km

Now, this distance will be covered at the rate of 90 km/hr.

∴ time taken = \(\frac{45}{90}\) = \(\frac{1}{ 2}\)hour
Total time = 4 + \(\frac{1}{ 2}\) = 4 \(\frac{1}{ 2}\)hours

1. A man starts from a place P and reaches the place Q in 7 hours. He travels 1/4 th of the distance at 10 km/hour and the remaining distance at 12 km/hour. The distance, in kilometer, between P and Q is:

    A. 70 km

    B. 72 km
    C. 80 km
    D. 90 km


Answer: Option C

Explanation: Let one-fourth of the distance between P and Q be x km

then

Time taken for the first one-fourth distance = \(\frac{×}{10}\) km/hour
and

Time taken for the remaining distance = \(\frac{2×}{12}\) km/hour
Since Total time taken is 7 hours ⇒ 7 = \(\frac{×}{10}\) + \(\frac{3×}{12}\)

On solving, x = 20

Total distance = 4x = 80 km.


2. In the school, Mohan and Govind took a part in the race and the ratio between their speeds is 5 : 7. Mohan losses the race by 360m then what is the length of the track (in km)?

    A. 1.26 km
    B. 1.2 km

    C. 2 km
    D. 0.9 km


Answer: Option A

Explanation: t = \(\frac{D}{S}\)
According to the question,

Let Speed = 5x, 7x Distance = y m
\(\frac{y – 360}{5×}\) = \(\frac{y }{7×}\)
\(\frac{y – 360}{5}\) = \(\frac{y }{7}\)
7 (y – 360) = 5y

7y – 5y = 2520

2y = 2520

y = 1260

= 1.26 km.


3. The respective ratio between the speed of a car, a train, and a bus is 5 : 9 : 4.The average speed of the car , the bus and the train is 72 km/hr together. What is the average speed of the car and the train together?

    A. 82 km/h
    B. 72 km/h
    C. 84 km/h
    D. 67 km/h


Answer: Option C

Explanation:Let speed of the car, the train, and the bus be 5a Km/hr , 9a Km/hr and 4a Km/hr respectively.

Given, total speed = (72 × 3) Km/hr = 216 Km/hr

⇒ 5a + 9a + 4a = 216

⇒ 18a = 216

⇒ a = 12Km/hr

⇒ speed of car = 5 × 12 = 60 Km/hr

And

speed of train = 9 × 12 = 108 Km/hr

⇒ their average speed = \(\frac{60 + 108}{2} \) = 84 Km/hr


4. Ranvir goes to his office from his house at a speed of 16 km/hr and returns to his home from his office at a speed of 20 km/hr and he takes 4 hour 30 minutes in all. If the distance of his friend’s house from his office is 20% more than the distance of his house from his office, find the distance of his house to his friend’s house.(assuming the office lies between Ranvir’s house and his friend’s house)

    A. 80 km
    B. 60 km
    C. 92 km
    D. 88 km


Answer: Option D

Explanation: Let the distance of his house to his office = D km

T = \(\frac{D}{S}\)
4 hour 30 minutes =\(\frac{D}{16}\)+\(\frac{D}{20}\)
\(\frac{9}{2}\) = \(\frac{5D + 4D}{80}\)
\(\frac{9}{2}\) = \(\frac{9D}{80}\)
D = 40

The distance from his house to his office = 40 km

The distance from his office to his friend’s house = 40 km × 120% = 48 km

The distance from his house to his friend’s house = 40 + 48 = 88 km


5. Mohit and Anuj took a part in a race. Mohit runs 300m in 50 second and Anuj takes 1 minute to cover the same distance. By what distance will Mohit beat Anuj in 300 m race?

    A. 25 m
    B. 55 m
    C. 60 m
    D. 50 m


Answer: Option D

Explanation: Mohit runs 300m in 50 sec.

Anuj runs 300m in 60 sec.

Now, In 1 sec Anuj runs 5m

Therefore, in 50 sec Anuj runs 50×5 = 250m

Mohit beats Anuj by 300 – 250 = 50m



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