Aptitude Questions

1. One guy has Rs. 100/- in hand. He has to buy 100 balls. One football costs Rs. 15/, One Cricket ball costs Re. 1/- and one table tennis ball costs Rs. 0.25 He spend the whole Rs. 100/- to buy the balls. How many of each balls he bought?  

2. The distance between Station Atena and Station Barcena is 90 miles. A train starts from Atena towards Barcena. A bird starts at the same time from Barcena straight towards the moving train. On reaching the train, it instantaneously turns back and returns to Barcena. The bird makes these journeys from Barcena to the train and back to Barcena continuously till the train reaches Barcena. The bird finally returns to Barcena and rests. Calculate the total distance in miles the bird travels in the following two cases: 
   (a) The bird flies at 90 miles per hour and the speed of the train is 60 miles per hour. 
   (b) the bird flies at 60 miles per hour and the speed of the train is 90 miles per hour 
   

3. A tennis championship is played on a knock-out basis, i.e., a player is out of the tournament when he loses a match. 
   (a) How many players participate in the tournament if 15 matches are totally played? 
   (b) How many matches are played in the tournament if 50 players totally participate? 
   

4. When I add 4 times my age 4 years from now to 5 times my age 5 years from now, I get 10 times my current age. How old will I be 3 years from now?   
   

5. A rich merchant had collected many gold coins. He did not want anybody to know about them. One day, his wife asked, "How many gold coins do we have?" After pausing a moment, he replied, "Well! If I divide the coins into two unequal numbers, then 37 times the difference between the two numbers equals the difference between the squares of the two numbers."  The wife looked puzzled. Can you help the merchant's wife by finding out how many gold R
   

6. A set of football matches is to be organized in a "round-robin" fashion, i.e., every participating team plays a match against every other team once and only once.  If  21 matches are totally played, how many teams participated? 
   

7. Glenn and Jason each have a collection of cricket balls. Glenn said that if Jason would give him 2 of his balls they would have an equal number; but, if Glenn would give Jason 2 of his balls, Jason would have 2 times as many balls as Glenn. How many balls does Jason have? 
   

8. Suppose 8 monkeys take 8 minutes to eat 8 bananas. 
   (a) How many minutes would it take 3 monkeys to eat 3 bananas?
   (b) How many monkeys would it take to eat 48 bananas in 48 minutes      
   

9. It was vacation time, and so I decided to visit my cousin's home. What a grand time we had! In the mornings, we both would go for a jog. The evenings were spent on the tennis court. Tiring as these activities were, we could manage only one per day, i.e., either we went for a jog or played tennis each day. There were days when we felt lazy and stayed home all day long. Now, there were 12 mornings when we did nothing, 18 evenings when we stayed at home, and a total of 14 days when we jogged or played tennis. For how many days did I stay at my cousin's place? 
   

10. A 31" x 31" square metal plate needs to be fixed by a carpenter on to a wooden board. The carpenter uses nails all along the edges of the square such that there are 32 nails on each side of the square. Each nail is at the same distance from the neighboring nails. How many nails does the carpenter use? 

 Answer and Explanation.

1.    F + C + T = 100-------------eq1
      15F + C + 0.25T = 100-------------eq2
      eq1=eq2 .solve to get F=3T/56 ;F=3,T=56,C=41
   

2. a) There is no need to consider their meeting pt at all.the train has been running for 90miles/(60miles/hr)=1.5hrs.bird flies till train reaches destination frm strting pt.so bird flies for1.5hrs at the vel given(90).so dist=1.5*90=135miles 
   
    b)  time of train=1hr.so dist of bird=60*1=60miles
   
   

3. (a) u don't need to sum it up.since it's a knock out only 1 person emerges winner finally.so15+1=16is answer.becos after15 matches finally we shud've 15losers and 1winner.
   
   (b)  49:its always one less than no of players as per the idea  given above.so no need to check okay cos its always true.ans is 49. 
   

4.  Let x= current age 
    4(x+4)+5(x+5)=10x ;so x=R 41 years
   

5. 37(x-y)=x^2-y^2. u no tht x^2-y^2=(x-y)(x+y).so (x-y) cancels on both sides to give x+y=37.so sum of unequal halves=37 which is the req answer.
   

6. R ans:7 teams okay.for a match u need 2 teams.suppose there r totally 'n 'teams.
   Now uve to choose 2 teams out of 'n' teams.so answer =no of such choices=no. of possible combinations. So we've ans = nC2(ncombination2)=21;solve to get n=7.
   Sol: n(n-1)/2=21. so n=7.if u don't understand c the graph below
   each team plays no. of matches=no of teams ahead of it. One bar '|' represents one team.
   | | | | | | | ------------7 
   6 5 4 3 2 1 0 -----------21
   last team is written as 0 matches becos this team has already played with all other teams-hence sum of matches =6+5+4+3+2+1=21 which is correct only if no of teams =7
   

7. R 14
   1. G+2=j-2
   2. 2(G-2)=J+2.
   solve these 2 to get 
   J=14
   

8. a). Sol:each mky takes 8 min to eat a banana 
   
    b).ans:8m=48 m=6
   

9. Use sets and venn diagram to solve such questions.a,b ,aub,anb etc.
   12=tennis+leave
   18=jog +leave
   so jog-tennis=6
   again jog+tennis=14.so solve and get jog=10,leave=8,tennis=4.so tot=22
   

10. Ans= 32*2 + 30*2=124