Written Test Date: 27th June 2004 0900 Hours
Venue: La Marts Boys Kolkata, Full Marks: 50
1. The time a passenger train takes to cross another freight train is twice when the passenger train crosses the freight train running in opposite directions. What is the ratio of their speeds?
2. In a container A wine is half filled. In another container B, twice the capacity wine is one fourth filled. They are then filled with water and poured in container C. What is the proportion of wine in container C?
3. There are N stations and tickets are issued from all the stations to the other stations. When some more stations were added to the route then 46 more tickets were introduced. How many are some? How many initial stations were there?
Ans: 11 and 2
4. Ten students in a class of 100 do not take up either physics or chemistry. 75 of them atleast take up physics, 83 take up atleast chemistry. How many take up both physics and chemistry?
5. The age of A when reversed becomes B's age. when age of B is taken away from A it is twice C's age. B's age is ten times that of C's. What are their ages?
Ans: A=54; B=45; C=4.5
6. A woman gave a man for his trust half the amount of pennies in her purse and one penny more. She gave another man half of the remaining amount and two pennies more. She gave yet another half of the remaining amount and three pennies more. And now she has only one penny remaining in her purse. How many pennies did she have initially?
7. In the construction of a house these were required
Designer and Painter equals Rs. 1100
Painter and Plumber equals Rs. 1700
Plumber and Electrician equals Rs. 1100
Electrician and Constructor equals Rs. 3200
Constructor and Mechanic equals Rs. 5300
Mechanic and Painter equals Rs. 3200
What are their individual costs?
Ans: Designer=200; Painter=900; Plumber=800; Electrician=300; Constructor=3000; Mechanic=2300
8. Three persons A, B, c run a race. They belong to the following categories not in order: Sororean, who always told the truth; Nororean, who always told lies and Midrorean who told lies and truth alternatively but not necessarily in this order. After the race they said the following.
1) C has interrupted me in the race.
2) B has won the race.
3) I have not won the race.
1) I have not won the race.
2) A has won the race.
1) B has won the race.
2) I have not interrupted A in the race.
To which categories did they belong?
Ans: A=Nororean; B=Sororean; C=Midrorean
9. Tom has a martian friend named Dorman who got lost. He learnt their language and asked three martians named Aken, Bak, and Cwon who belonged to the categories Uti (who always spoke the truth), Yumi (who always lied) and Grundi (sometimes truth / sometimes lied). Tom asked them two questions viz. Which category do you belong? Which category does Dorman belong?
- Aken replies
I am not an Uti.
Dorman is not a Grundi.
- Bak replies
I am not an Uti.
Dorman is not a Yumi.
- Cwon replies
I am not a Grundi.
Dorman is not an Uti.
(There was probably a printing Error but answer could be easily inferred)
Ans: Dorman is 'Uti'
10. (This was the toughest question and no one in my knowledge was confident of the correct answer)
At the scene of the murder there is a Witness, Victim, Murderer, Policeman, Judge, and Hangman. The witness did not see the shooting but heard an altercation before the victim was shot to death. The murderer was convicted and finally hanged to death. The persons are Fillip, Clark, Hunt, Walt, Graham and Bill.
1) Hunt and Walt never met.
2) the policeman picked up Graham from the scene of the crime.
3) Bill was the last to see Fillip alive..
4) Clark was asked by the judge to give his account of the shooting.
5) Hunt knew both the victim and the murderer
Identify who was who?
Ans: Only Fillip is the victim can be properly inferred.