List of top Mathematics Questions on Time, Speed and Distance

Mohan can reach his destination on time by travelling at a speed of 54 km/hr. If one-fourth of the time, he covers \( \frac{2}{9} \) of the total distance, at what speed should the remaining distance be travelled so as to reach his destination on time?
Statement: There must be more than one High Court in each state in India.
Arguments:
I. This will be a sheer wastage of taxpayers’ money.
II. This will help to reduce the backlog of cases pending for a very long time.

Which of the following is the correct answer?
Statement: All successful businessmen are good in time management.
Conclusions:
I. All the people who manage the time effectively are successful businessmen.
II. A successful businessman cannot afford to waste time.
In the year 2024, the Department Store P had a sales total for December that was 4 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year?
A certain bridge is 4,024 feet long. Approximately how many minutes does it take to cross this bridge at a constant speed of 20 miles per hour? (1 mile = 5,280 feet)
About three towns A, B, and C, the information available are: A’s population is twice as B and C’s population is half times as B. Then A’s population compared to C is
Two buses start at 9AM from two different places on a straight road. The buses travel towards each other at uniform speeds of 45 kmph and 55 kmph respectively. If the two places are 200 km apart, the buses will meet at
A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds and him in 8 seconds. The length of the train is:
A train moving at a speed of 63 km/hr enters a railway station and crosses the platform in 20 sec. If the length of the train is 100 m, what is the length of the platform?
A 100 m long train is moving at a speed of 60 km/h. Then the train will cross a signal pole in
A system consists of N particles, interacting with each other (for example, protein molecules). Which one of the following statements is FALSE?
Three pipes A, B, and C can fill a tank in 6 hrs. After working at it together for 2 hrs, C is closed and A and B can fill the remaining part in 7 hrs. The total number of hours taken by C alone to fill the tank is
Let \( A \) be a \( 2 \times 2 \) non-diagonalizable real matrix with a real eigenvalue \( \lambda \) and \( v \) be an eigenvector of \( A \) corresponding to \( \lambda \). Which one of the following is the general solution of the system \( y' = Ay \) of first-order linear differential equations?
Let \( A \) be a \( 3 \times 3 \) real matrix and \( b \) be a \( 3 \times 1 \) real column vector. Consider the statements:
1. The Jacobi iteration method for the system \( (A + \epsilon I_3)x = b \) converges for any initial approximation and \( \epsilon>0 \).
2. The Gauss-Seidel iteration method for the system \( (A + \epsilon I_3)x = b \) converges for any initial approximation and \( \epsilon>0 \).
Which one of the following is correct?
A car travelling with $\frac{2}{5}$ of its actual speed covers 400 km in 16 hours 40 minutes. Find the actual speed of the car.
Two cyclists start together to travel to a certain destination, one at the rate of 4 kmph and the other at the rate of 5 kmph. Find the distance if the former arrives half an hour after the latter.
A student walks from his house at \( \frac{5}{2} \) km/h and reaches his school late by 6 minutes. Next day, he increases his speed by 1 km/h and reaches 6 minutes before school time. How far is the school from his house?
Two cyclists start together to travel to a certain destination, one at the rate of 4 kmph and the other at the rate of 5 kmph. Find the distance if the former arrives half an hour after the latter.
The number that must be added to each of the numbers 8, 21, 13 and 31 to make the ratio of the first two numbers equal to the ratio of the last two numbers is
The work done by a woman in 8 hours is equal to the work done by a man in 6 hours and by a boy in 12 hours. If working 6 hours per day, 9 men can complete a work in 6 days, then in how many days can 12 men, 12 women and 12 boys together finish the same working 8 hours per day?
A runs \( 1 \frac{2}{3} \) times as fast as B. If A gives B a start of 80m, how far must the winning post be, so that A and B might reach it at the same time?
A ball is thrown from the top of a building of height 25 m with an initial velocity of 15 m/sec. If the height of the ball h from ground at any point of time t is given by \(h=25+10t-3t^2\). The time taken by the ball to reach the ground is
A man rows 1 km upstream in 20 min and 1 km downstream in 15 min. What is his speed of rowing in still water?
A man takes 5 hours to walk to a certain place and returns by car. He would have, however, gained 3 hours if he had completed his entire journey by car. How long would he have taken to walk both ways?
A man covers a certain distance on a toy train. If the train moved 4 km/h faster, it would take 30 min less. If it moved 2 km/h slower, itwould have taken 20 min more. What is the distance covered?