TSD Questions - Test 1

Q1. Bell and Bolt run at speeds of 9 m/s and 9.9 m/s respectively on a 105-meter-long circular track. They start simultaneously from the same point and run in opposite directions. How many times would they have met by the time Bolt covers 600 m?

Q2. Two towns A and B are 100 km apart. A school is to be built for 100 students of town B and 30 students of town A. Expenditure on transport is Rs 1.20 per km per student. If the total expenditure on transport by all 130 students is to be as small as possible, then the school should be built at.

Q3. The Rajdhani Express travels a distance of 400 km. If however, it travels a distance of d km at the normal speed and the remaining distance at 3/4th of its normal speed, then it is late by an hour. If it travels a distance (d + 50) km at 3/4th of its normal speed and the remaining distance at normal speed, then it is late by half an hour. Find d and the train’s normal speed.

Q4. In a race of 200 metres run, A beats S by 20 metres and N by 40 metres. If S and N are running a race of 100 metres with exactly same speed as before then, by how many metres will S beat N?

Q5. Three runners A, B and C run a race, with runner A finishing 12 metres ahead of runner B and 18 metres ahead of runner C, while runner B finishes 8 metres ahead of C. Each runner travels the entire distance at constant speed. What was the length of the race?

Q6. Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is.

Q7. Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to catch a train arriving there from B. He must reach C at least 15 minutes before the arrival of the train. The train leaves B, located 500 km south of A, at 8:00 am and travels at a speed of 50 km per hour. It is known that C is located between west and north-west of B, with BC at 60° to AB. Also, C is located between south and south-west of A with AC at 30° to AB. The latest time by which Rahim must leave A and still catch the train is closest to.

Q8. A policeman was chasing a thief who was running at 20 km/hr. The distance between the policeman and the thief was 80 km when the policeman started chasing. If the policeman caught the thief in 4 hours, find the speed of the policeman.

Q9. In a 500 m race, L beats M by 40 seconds and beats N by 125 m. If M and N run a 500 m race, M beats N by 40 seconds. Find the time (in seconds) taken by L to run the race.

Q10. A man and his son go to a park. Seeing children of his age group, the son starts running and the man also starts running trying to catch him. The man takes 4 paces in the time his son takes 10 paces. The son covers 0.5 m per pace whereas the man covers 1.3 m per pace. How many paces should the man take to catch up with his son who is 9 m ahead?

Q11. Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are 60 km apart. If the speed of one of the ships is 6 km per hour more than the other one, then the speed, in km per hour, of the slower ship is.

Q12. If a man cycles at 10 km/hr, then he arrives at a certain place at 1 pm. If he cycles at 15 km/hr, he will arrive at the same place at 11 am. At what speed must he cycle to get there at noon?

Q13. The winning relay team in a high school sports competition clocked 48 minutes for a distance of 13.2 km. Its runners A, B, C and D maintained speeds of 15 kmph, 16 kmph, 17 kmph, and 18 kmph respectively. What is the ratio of the time taken by B to time taken by D?

Q14. The guards of two goods trains A and B are in the respective last carriages of their trains. The speeds of A and B are 2m/sec and 3m/sec respectively. A and B have lengths of 200 m and 300 m, respectively. They enter a 500-metre-long tunnel from opposite ends. The guard of one of the trains wants to pick up a flag from the other guard. How long after the instant when the two trains begin to enter the tunnel does the transfer occur?

Q15. A petrol car consumes 10 litres of petrol travelling continuously for 2 hours at a speed of 50 km/hr. At 40 km/hr, a diesel car consumes 10 litres of diesel during 3 hours of travel. If the diesel car travels 540 km using a certain quantity of diesel at 40 km/hr, then what is the distance that the petrol car can travel using an equal quantity of petrol travelling at 50 km/hr?