11. Past Questions

Question 1

1) There is a tunnel connecting city A and B. There is a CAT which is standing at 3/8 the length of the tunnel from A. It listens to the whistle of the train and starts running towards the entrance where, the train and the CAT meet. In another case, the CAT started running towards the exit and the train again met the CAT at the exit. What is the ratio of their speeds?
[CAT 2002]

		$4 : 1$
		$1 : 2$
		$8 : 1$
		None of these

Question 2

2) Pradeep could either walk or drive to office. The time taken to walk to the office is 8 times the driving time. One day, his wife took the car making him walk to office. After walking 1 km, he reached a temple when his wife called to say that he can now take the car. Pradeep figured that continuing to walk to the office will take as long as walking back home and then driving to the office. Calculate the distance between the temple and the office.
[XAT 2016]

		$1$
		$\frac{7}{3}$
		$\frac{9}{7}$
		$\frac{16}{7}$
		$\frac{16}{9}$

Question 3

3) Mukesh, Suresh and Dinesh travel from Delhi to Mathura to attend Janmasthmi Utsav. They have a bike which can carry only two riders at a time as per traffic rules. Bike can be driven only by Mukesh. Mathura is 300Km from Delhi. All of them can walk at 15Km/Hrs. All of them start their journey from Delhi simultaneously and are required to reach Mathura at the same time. If the speed of bike is 60Km/Hrs then what is the shortest possible time in which all three can reach Mathura at the same time.
[IIFT 2010]

		$8 \frac{2}{7}$ hrs
		$9 \frac{2}{7}$ hrs
		$10$ hrs
		None of these