Time, Speed & Distance Level-3 Quiz-3

1. The village of Risalgarh has an annual bullock cart race. The final participants are required to cover the shortest path touching all the four entrances to the village, (S, E, N, W) located at the south, east, north and west, respectively different directions spaced equally on the circumference of a circle. One year there were just two finalists selected after the preliminaries. It was known that one of them was five times as fast as the other. If they start from S and go towards W (and beyond) where will they meet for the 23rd time, after they start?

2. Two soldiers A and B start from different points on a straight line. Initially A is to the south of B. They march north at uniform rates. When A covers 2 km, both make an about turn and start marching south at different uniform rates. 3 min later B arrives at A’s turning point. A arrives at his starting point, and continues to march south. One minute after A crosses his starting point, B reaches that point. How far south do they travel beyond A’s starting point by the time they meet?

3. M and N started running simultaneously around a circular track 8 km long in the same direction. The initial position of M was 2 km behind that of N. M met N for the first time after 2000 seconds when both were in their respective second rounds around the track. Had N travelled in the opposite direction, they would have met after 200 seconds. If M’s speed is 9 (1/11) % less and N’s speed is 11(1/9) % more and the two start simultaneously from the same point in opposite directions, they would meet after (time in secs)?

4. Diya and Riya started from X and Y towards Y and X, respectively. After reaching their destinations, they return to their respective starting points. After reaching their starting points, they again start towards Y and X, respectively. They continue this process infinitely. But every
time they meet, both decrease their speed by 30%. The first time they meet at 12 km from Y and the second time they meet at 6 km from X. If the speed of the faster one is less than twice the speed of the slower one, where will they meet for the third time?

5. Avinash starts from his hostel at 9:30 a.m. and walks towards a neighborhood sports complex. Sometime later, Bharat starts from the same hostel and walks towards the sports complex. A few minutes after that, exactly at 9:45 a.m., Chetan also sets off from the same hostel and walks to the sports complex, he arrives at the complex at 10:30 a.m., twenty minutes after that Bharat reaches the complex and 10 minutes later, Avinash also reaches the complex. At a certain time, all three happen to be at the same point on the route. When does Bharat start from the hostel?

6. The speed of the bus from the bottom of hill to the top is 10 kmph and it takes 8 hours more than the bus from the top to complete its trip. What is the distance between the top and the bottom of the hill?

7. Vicky and Nicky run back and forth between the town hall and the county station at respective speeds of 12 kmph and 18 kmph. They start simultaneously – Vicky from the town hall and Nicky from the county station. If they cross each other for the first time 14 minutes from
the start, at what distance from the county station do they cross each other for the fifth time?

8. A ship which was 154 km from the shore developed a leak in the hull, through which 41⁄2 tonnes of water started leaking into the ship every 11 minutes. When 184 tonnes of water enter the ship, the ship would start sinking. But the pumps can throw out 1 tonne every five minutes. Find the minimum average speed of the ship so that she may not sink.

9. A person walked along a 2 kms long circular track for 5 hours. He then cycled for twice as much time as he took to walk one round. He then rode a bike for as much time as he took to walk one round. He covered a total of 15 rounds in cycling and in the first 4 hours of walking. He covered a total of 17 rounds in riding his bike and in 5 hours of walking. If the speeds of his cycle and his bike were in the ratio 3 : 4, find the speed of his cycle.

10. Raju, who stays in city Z wants to catch a train at city Y. The train arrives at Y from city X which is 720 km directly to the south of Z. ZY and XY make angles of 60° and 30°, respectively with XZ. The train starts at X at 7:00 a.m. and travels at 90 3 km/hr, while Raju drives to Y at 60 km/hr. If Raju wants to be at Y at least 20 minutes before the arrival of the train, what is the latest time at which he can start from Z?