Time, speed, and distance and time and work are the most important topics under unitary methods. The main subtopics are relative velocity, circular tracks, boats, races, and escalators, and pipes and cisterns. The practice questions given below will be of great help in mastering these topics.

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Instructions

For the following questions answer them individually

Question 1

It takes 10 men and 20 women to complete a project in 48 days. After the first day, a woman was replaced by a man and it took them 45 more days to complete the work. If 10 men and 20 women had worked on the same project, and after 2 days, if 2 of the women had been replaced by 2 men, how many more days would it have taken to finish the project?Round up to the nearest integer.

Question 2

Ajay and Vijay race 2400 metres around a 400m circular track. Ajay is 50% faster than Vijay and gains a lap over him in 4 minutes. Find the time taken by Ajay to finish the race?

Question 3

The hands of two clocks coincide every 60 minutes and 72 minutes respectively. What is the approximate time difference between the two clocks (round to closest minute) after 24 hours as measured by a correct clock?

Question 4

Ajay, Alay and Vijay travel at 80, 50 and 40 km/hr. They start from the same point in the same direction. Ajay and Vijay started at 11 am and 5am respectively. If all three of them met at the same place at the same time, what time did Alay start?

Question 5

Ajay and Vijay are running towards each other at the same speed from A and B respectively. After running for some time, Ajay sprains his ankle at point C and walks at half his earlier speed. They finally meet at point D such that AD = $$\frac{4}{10}$$ AB. Find the ratio of $$\frac{AC}{AD}$$

Question 6

If a train overtakes two cyclists cycling at 15 km/hr and 20 km/hr, in the same direction as the train, in 72 seconds and 81 seconds respectively. Find the length of the train?

Question 7

Ajay and Vijay drive towards each other at 40 km/hr and 60 km/hr. They are initially 200 kms away. How far apart are they 3 minutes before they meet?

Question 8

In a 1000 metre race, A beats B by 30 seconds and B beats C by 20 seconds. By how much did A beat C?

Question 9

X and Y are walking from Town A to Town B, 50 km apart, at 6 kmph and 10 kmph respectively. If Y turns back immediately after reaching B and meets X at Town C, what is the distance between Town A and Town C?

Question 10

Three cities A,B,C are equidistant from each other. Jessi and Jackie started from cities A, B respectively towards city C. By the time Jessie traveled 60 kms, Jessie, Jackie and C form a right angled triangle. By the time Jackie reached C, Jessie is still 90 kms from C. If Jackie reached C in 3 hours, how much more time will Jessie take to reach C?

Question 11

In a 1000 metre race, A beats B by 30 seconds and B beats C by 20 seconds. By how much did A beat C?

Question 12

A tank has 3 inlet pipes and 2 outlet pipes. The inlet pipes can individually fill the tank in 4, 6 and 8 hours. The outlet pipes can individually empty the tank is 2 hours and 10 hours. Find the time in which the empty tank gets filled, if all the taps are kept open.

Question 13

Three people Kiran, Kumar, and Kishore started running from the same point on a circular track. Kiran and Kumar run in the same direction whereas Kishore runs in the opposite direction. When Kiran and Kishore meet for the first time, Kumar is diametrically opposite Kiran. What is a possible ratio of speeds of Kiran, Kumar and Kishore respectively?

Question 14

Ram and Shyam, who are standing 100 m away from each other, are throwing a Frisbee towards each other in a straight trajectory. Initially Ram has the Frisbee and as soon as he throws it towards Shyam, they both start moving towards each other. Shyam catches the Frisbee and throws it back to Ram and they keep throwing it until they meet each other. They both throw the frisbee at a speed of 20 m/s. If the frisbee travelled a total distance of 12 km and the speeds of Ram and Shyam are in the ratio of 2:3 respectively, find the speed of Shyam (in metres per min). (Assume that the time taken by Ram and Shyam to catch the frisbee and throwing it back again is negligible, and the frisbee travels at a uniform speed in the air)

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Question 15

Madhu went to a mall. While climbing an escalator at her normal speed, she noticed that she took 25 steps and it took her 60 seconds to reach the top. In the next run, she climbed at a speed double of that of the previous time and reached the top in 45 seconds. How much time will Madhu take to reach the top of a stationary escalator if she climbs at her normal speed?

Question 16

Two friends A and B meet at a point between their houses. Generally, they leave their respective houses at 7:50 AM and meet at 8:05 AM. One day, one of them, B started at 7:55 AM and met A at 8:07 AM. On the next day, if B started at 7:50 AM and had to travel all the way to Aās house, find the duration of time for which he walked.

Question 17

Ashu and Nitesh are running on a straight road whose end points are P and Q. Ashu starts from P and Nitesh starts from Q. Both of them run towards each other. On reaching the opposite points, they turn back and move towards P and Q again. This process keeps on repeating and they always meet when they are travelling in opposite directions.The first point where they meet is 720 metres away from P and the point where they meet for the second time is 800 m from Q. How far(in m) from Q is their third meeting point ? (They run with the same speed for the entire duration)

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Question 18

Elite rowers can row upstream from Haridwar to Rishikesh in 5 hours. The amount of time they take to row in still water for the same distance is 50 mins more than the time they take to row downstream. What is the time taken by them to row downstream from Rishikesh to Haridwar (given that it is greater than 2 hours)?

Question 19

Two trains, Garibrath express and Durunto express are moving towards each other on parallel tracks. The speed of Garibrath and Durunto express are 72 km/hr and 54km/hr respectively. Ram is sitting near the front end of Garibrath and Shyam is sitting near the rear end of Durunto express. As soon as the trains start crossing each other, Ram starts moving towards the rear end of Garibrath at the speed of 3 m/s and Shyam starts to move towards the front end of Durunto at the speed of 4 m/s. If the lengths of Garibrath and Durunto express are 120 m and 180 m respectively. After how much time(in seconds) from the instant that trains start crossing each other, will Ram and Shyam cross each other?

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Question 20

There are 100 people in a group. Each person, while working individually, can complete a piece of work in 100 days. One person starts working on the project. On the second day, another person joins him, on the third day, one more person joins the first two and this process goes on till the work is completed. On which day does the work get completed?

Question 21

In 1 km race, in which A,B, C are running, A beats B by 100 m, B beats C by 100 m. In the next kilometer race, C starts at the starting line, B starts 100 m behind the starting line and A starts 100 m behind B. Find the distance (in m) by which the winner is ahead of the person just behind him.

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