Time, Speed & Distance Level-3 Quiz-1

1. In a 500 m race, A beats B by 40 m. In a 1000 m race, B beats C by 40 m. If A beats C by 14 6 seconds in a 500 m race, find the time taken (in minutes) by B to run 2.4 km.

2. Two students started simultaneously from the same point on a circular track and ran at speeds of 20 km/hr and 30 km/hr. Find the number of distinct meeting points where they meet if they are running in the same direction(s).

3. Vijay and his girlfriend started on a boat from a point on a river and began to row upstream. After rowing for two hours, Vijay stopped the boat. He wanted to hand over a flower to his girlfriend but it slipped from his hand into the river and floated downstream. They rowed upstream
for two more hours and then turned back. They caught up with the flower, at a point 6 km downstream of the point at which it fell into the river. Find the speed (in km/hr) of the stream.

4. Every day, Hari drives his motorcycle at a certain speed and reaches his office exactly on time. One day, after travelling a certain distance, he slowed down to 3/4 th of his initial speed and arrived at his office 6 minutes late. Had he slowed down to 2/3 rd of his initial speed 6 km
further on, he would still have reached 6 minutes late. What is his initial speed (in km/hr)?

5. Two people can run around a circular track in 30 s and 60 s. If they start simultaneously in the same direction from diametrically opposite points, After how many seconds will they meet for the second time?

6. A bus covers a certain distance every day at an uniform speed. One day, after covering 30% of the distance, its speed decreased and the bus reached its destination 10 hours late. Had the decrease in speed occurred after the bus had covered 70 km more, it would have been late by
only 9 hours. Find the distance covered by the bus every day.

7. Three cyclists Rona, Sona and Tina start from Battisgarh to Chattisgarh at 8.00a.m., 9.00a.m. and 10.00a.m., respectively. The distance Tina travels to meet Sona is twice the distance she travels to meet Rona. By the time Tina reaches Chattisgarh, Sona is twice as far from Rona as she
is from Tina. If the ratio of the speeds of Sona and Tina is 2 : 3, at what time does Rona reach Chattisgarh?

8. Three runners A, B and C run around a circular track at different speeds. They start at the same point, but while A and B run clockwise, C runs anticlockwise. All 3 go around the track several times. It is found that between A and B, the faster overtakes the slower at 3 different points. A and C cross each other at 7 different points and B and C cross each other at 10 different points. What could be the ratio of the speeds of A, B and C?

9. Ajay and Sanjay start simultaneously from the same point on a circular track. If they travel in opposite directions, they meet at 7 distinct points on the track whereas if they travel in the same direction, then they meet at n distinct points on it where n is a prime number. If Ajay is faster
than Sanjay and Sanjay’s speed is P% less than that of Ajay, then which of the following can be a value of P?

10. Two cities X and Y lie on a straight line. Two men P and Q left simultaneously for Y and X from X and Y, respectively. P reaches Y and immediately turns around and moves towards X. On reaching X, again he turns around and moves towards Y. This kind of movement continues indefinitely. Q also travels in a similar manner. The distance between X and Y is 1000 m and the ratio of the speeds of P and Q is 3 : 2. Find the distance travelled by P when he meets Q for the 4 th time.