First Naukri Speed, Time and Distance, Boats and Streams Quiz -1

Solution:

Speed of Manjishtha = 5 kmph, speed of Kiran = 45 kmph

Distance between them = 320 km

Relative speed = 45 + 5 = 50 kmph

Time taken = \frac{320}{50} = 6.4 hours

They start at 6 am. So, they will meet at 12:24 pm.

Solution:

Ankita and Arpan complete one round in 12 seconds and 16 seconds respectively.

∴ Speeds of Ankita and Arpan are \frac{960}{12} and \frac{960}{16} i.e. 80 m/s and 60 m/s respectively.

Relative speed of Ankita with respect to Arpan = (80 – 60) m/s = 20 m/s

Hence, Ankita meets Arpan after every \frac{960}{20} = 48 seconds

To complete 14.4 km, number of rounds required = \frac{144}{0.96} = 15

Since Ankita is faster, she will win the race, and therefore race time = 15 \times 12 = 180 seconds

Since both of them meet each other after every 48 seconds, after the start, Ankita will meet Arpan 3 times during the race.

The time when both of them will meet for the last time = 48 \times 3 = 144 seconds

Solution:

During normal hours, the speed of Harbhajan

= \frac{136}{2} = 68 km per hour

During peak hours, his speed = 80% of 68 = 54.4 km per hour

The total time taken by him to travel 190.4 km during normal hour = \frac{190.4}{68} = 2.8 hours

The total time taken by him to travel the same distance during peak hour = \frac{190.4}{54.4} = 3.5 hours

The total time taken by him in the journey = (3.5 + 2.8) = 6.3 hours = 6 hours 18 minutes

Solution:

Let us say Ashwin meets Hanks after ‘t’ seconds he starts from the starting point. Speeds of Ashwin and Hanks are 5 m/s and 2.5 m/s.

t = \frac{1000}{5 - 2.5} = 400 seconds

Distance traveled by Ashwin when it meets Hanks for the first time = 2000m i.e., after 2 complete revolutions. Ashwin can make 10 complete revolutions. As he meets Hanks after every two revolutions he would meet Hanks after the 10th revolution for the last time i.e., after 400 \times 5 = 2000 seconds

Solution:

Let the speed of the boat in still water and speed of stream be 5x and 2x respectively.

According to the question,

\frac{224}{4}  = 5x + 2x

x= \frac{32}{4} = 8

Required difference = 5x – 2x = 3x

3x = 24 km/hr

Solution:

Let the speed of the boat in still water be s m/sec

As the object covers 100m in 50 sec, so the distance traveled by the object will be with the help of the

speed of the stream only.

Speed of stream = \frac{100}{50} =  2 m/s

Given that,

(s – 2) = (s + 2) – \frac{50 (s + 2)}{100}

(s – 2) = (s + 2)(1 – 1/2)

s = 6 m/sec

s= \frac{6 \times 18}{5} = \frac{108}{5} km/hr

Distance covered by the boat in still water in 5 hours = 108 \times \frac{5}{5} = 108 km

Solution:

At Home                    At Restaurant

Actual Time -     12:00 -------------------------------------- 2:00------------2:30

Wristwatch time - 12:30---------------------------------------2:30

As per wristwatch Arun leaves Home at 12 : 30PM and arrives at restaurant at 2 : 30PM

Wristwatch is 30 minutes ahead so he leaves at 12 : 00 noon and arrives at 2 : 00 PM

Journey Time (T’) = 2 hrs

Actual journey time (T) = 2hrs 30min

Time is inversely proportional to speed

\frac{T'}{T} = \frac{S’}{S}

So, \frac{S'}{S} = \frac{5}{4}

Increase in speed = \frac{5 – 4}{4} \times 100%= 25%

Hence he increased his average speed by 25%

Hence, the correct answer is 25%

Solution:

Let the boy catch the bus after ‘t’ seconds

Speed of the boy = 20 km/hr

\frac{20 \times 5}{18} m/s = \frac{50}{9} m/s

Speed of the bus = 3 m/s

The time taken by the boy to catch the bus = \frac{460}{\frac{50}{9} - 3}

= 180 secs

Solution:

Virat’s speed = \frac{500}{3} % = \frac{5}{3} times Ashwin’s

Let the length of the race be x m.

Let Ashwin’s speed be 3s m/s and Virat’s speed be 5s m/s

According to the question,

\frac{x}{5} = \frac{x-200}{3}

⇒ x = 500 meters

Solution:

In still water, the speed of steamer = \frac{12000}{25}

= 480 meter per minute = 8 meters per second

Let the speed of stream = v m/sec

In upstream, the speed of steamer = (8 – v) m/sec

In downstream, the speed of steamer = (8 + v) m/sec

According to the question,

\frac{11250}{8 - v} - \frac{11250}{8 + v} = 12.5 \times 60 = 750 secs

By solving, v = 2 meters per second

\frac{2 \times 18}{5} = 7.2 km/hour