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Infosys Placement Puzzles - II (Ten Puzzles completely solved )

1) There are two taps, which are used to fill the tank and one tap to empty the tank. First tap fill the tank in 10 min., while the second takes quarter of an hour to fill the tank if both are operated independently.Third tap is capable of emptying the tank in seven and a half minutes. If all the taps are opened simultaneously how long (if ever) will it take for the tank to get filled completely? 
Ans
Pipe A fills the tank in 10 min
Pipe B fills the tank in 15 min
Pipe C empties the tank in 15/2 min

If all the three opened simultaneously then in 1 min
1/10 + 1/15 - 2/15 of the tank will be filled
that means 1/30 th of the tank will be filled in 1 min
So it will take 30 minutes to fill the tank completely if all three pipes opened

2)One thief entered a cave where he found a pile of diamonds. At first he thought of taking all. But listening to his conscience he thought of taking only half of them. But while returning he picked up two more from the pile. After that Second thief entered the cave and bagged half of remaining diamonds and picked up two more while returning. Later third thief entered and did the same. Even the fourth thief did the same. When the fifth thief entered he found only one diamond in the cave. How many diamonds are there in the cave at first.
Ans
Total diamonds in the cave at first = x
First thief took x/2 +2 So remaining is x/2 - 2 i.e (x-4)/2
Second thief took (x-4)/4 + 2 he left (x-4)/4 -2 i.e (x-12)/4
Third thief took (x-12)/8 + 2 he left (x-12)/8 -2 i.e (x-28)/8
Fourth thief took (x-28)/16 + 2 he left (x-28)/16 -2 i.e (x-60)/16

Now the remaining diamonds after fourth thief left is given as 1
So (x-60)/16 = 1
that means x = 76

3) There were two clock one is getting slow by two minutes/hr and another one is  gaining 1 minute every hour and exactly after how many hours there two clock has a 1hr difference.
Ans
First hour First clock slowed down by 2 min while second clock gains 1 min
So the time differerence after 1 hr it is 3 min
That means simply after 20 hours the time difference will be 1 hour between two clocks

4) A taxi driver states that his cab number  is divisible by the no 2,3,4,5,6 with a remainder of 1 and when  the number is divided by 11 it does not give any remainder
Ans
Find LCM of 2,3,4,5 & 6 that will give a number exactly divisible by 2,3,4,5, & 6
if you add 1 to any multiple of that number you will find it will satisfy the first condition
Now 61 not divisible by 11
but 120+1, 121 is exactly divisible by 11 So thats the answer

5) A man says that he gained 10  percent as profit in selling a suitable  cloth material. He says if he had purchased the same one 10 percent cheaper than it was actual and if he had sold  it for 20%  profit he gets 25paise less. find at what price he sold the suit.?
Ans
Assume CP as Rs.100 and he sold for Rs.110 for 10% profit
Now if CP is Rs.90 (10% cheaper) and Sold for Rs.108 (20% Profit) he got 2 Rupees less than actual
For 100 CP 2 Rs less Then for what CP .25 Rs less
100:x :: 2:.25
x = 100/8 which equal to 12.5
Ans
6) Today is Saturday. A person wants to meet a lawyer and as that lawyer is busy he asks him to come three days after the before day of the day after tomorrow? On which day the lawyer asks the person to come?
Ans
Today is Saturday.  Day after tomorrow will be Monday. Day before day after tomorrow must be Sunday. Then Three days after the day before the day after tomorrow is Wednesday. Thats the answer.

7)A person travels at a speed of 10 mph from one city to another. However while returning as there was  not much traffic. He  came with a speed of 15mph. what is his average speed? 
Ans
Average Speed = Total distance travelled/Total Time Taken
If x is the distance between cities
then Avg Speed = 2x/[(x/10)+(x/15)]
Then Average Speed is 12 mph

8)A women in her conversation said " if u reverse my own age, in figures represent  my husbands age. he is of course senior to me and difference between  our age is one 0ne-eleventh of their sum. what is the woman's and her husbands age? 
Ans
Let us take xy is the age of the women in figure
that means in value it is 10x+y
Also given 10y + x is the husbands age
10y+x - [10x+y]  = 1/11(10x+y+10y+x)
9y - 9x = x+y
8y = 10x
y= (10/8)x
So x should be 4 and y should be 5 ( Note x and y should be integers)
Womens age is 45 and husbands age is 54

9) There was a person who smoked a lot .One day he decided to quit his habbit,but he had 27 cigarettes with him.So he started smoking them one by one ,to finish them. He had the habit of  smoking only 2/3rd of it and leaving the rest butt. Latter he found out that by joining 3 butts he can form 1 cigarette. So ,tell how many cigarettes in all he smoked.
Ans 
From 3 butts he get 1 cigarette.Hence from 27 butts he get 9 (27/3) cigarettes. Then from 9 butts he gets 3 cigarettes  and from 3 butts he gets 1 more cigarette   27+9+3+1=40
So he smoked 40 cigarettes

10) There are some students in a school.The 1/2 of number of students is a whole number. The 1/6 of number of students is a whole number. The 1/5  of number of students is a whole number. The 1/7 of number of students is a whole number.Find the number of students.
Ans
The number of students in the school is exactly divisible by 2,5,6 & 7
So Find LCM of 2,5,6 & 7 which equal to 210
The number of students in the school is any multiple of 210