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Thursday, April 18, 2013

An Old Lamp And A Rug Puzzle

Puzzle

Mrs. Watsherface had a garage sale. A customer named Gina bought an old lamp and a rug. She paid a total of $5.25 for everything. The rug cost 25 cents more than the lamp.
 
How much did each cost?

Answer

The lamp cost $ 2.50 and the rug cost $ 2.75

Assume that the lamp cost $ L.

Hence the rug must have cost $ (L + 0.25)

Also, total cost is $ 5.25, Hence the equation :
L + L + 0.25 = 5.25
2 * L = 5
L = 2.50
Hence, the lamp cost $ 2.50 and the rug cost $ 2.75



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Wednesday, April 17, 2013

Two Trains Starting At Same Time Puzzle



Puzzle

Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination 1hr and 4hrs respectively after passing each other. How much faster is one train from other?

Answer

 

The speed of Bangalore-Mysore train is TWICE the speed of Mysore- Bangalore train.
 

Let the distance between Bangalore and Mysore is D kms.

Also, let speed of the train from Bangalore to Mysore is X km/hr and speed of the tain from Mysore to Bangalore is Y km/hr.


Now, assume that both the trains met each other at T kms from the Bangalore (point P in figure).


Time taken by Bangalore-Mysore train to reach P = Time taken by Mysore-Bangalore train to reach P
( T / X ) = ( D - T ) / Y -----equ(I)


Also, Bangalore-Mysore train and Mysore-Bangalore train arrive destination 1 hr and 4 hrs respectively after passing each other. It means that Bangalore-Mysore train travels (D - T) kms in 1 hr at X km/hr and Mysore-Bangalore train travels T kms in 4 hrs at Y km/hr. 


Hence,
( D - T ) = X and T = 4 * Y


Substituting these values in equation I, we get
( 4 * Y ) / X = X / Y
4 * Y * Y = X * X
2 * Y = X
Hence, the speed of Bangalore-Mysore train is TWICE the speed of Mysore-Bangalore train.





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Tuesday, April 16, 2013

Psychology & Business Majors Puzzle

Puzzle

All of the students at a college are majoring in psychology, business, or both. 73% of the students are psychology majors, & 62% are business majors.

If there are 200 students, how many of them are majoring in both psychology & business?

Answer

70 students are majoring in both, psychology & business.

If 73% of the students are psychology majors, we know that 27% are not psychology majors. 

By the same reasoning, 38% are not business majors, because 62% of the students do major in business. So: 27 + 38 = 65

65% of the students are not majoring in both psychology & business, so 35% are double majors, a total of 70 students.
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Monday, April 15, 2013

Round Trip Travel Time Of An Emergency Vehicle

Puzzle

An emergency vehicle travels 10 miles at a speed of 50 miles per hour. How fast must the vehicle travel on the return trip if the round-trip travel time is to be 20 minutes?





Answer

75 miles per hour
 
While going to the destination, the vehicle travels 10 miles at the speed of 50 miles per hour. So the time taken to travel 10 miles is
= (60 * 10) / 50
= 12 minutes

Now it's given that round-trip travel time is 20 minutes. So the vehicle should complete its return trip of 10 miles in 8 minutes. So the speed of the vehicle must = (60 * 10) / 8
= 75 miles per hour
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Sunday, April 14, 2013

Stations On A Railroad Puzzle

Puzzle


There were N stations on a railroad. After adding X stations 46 additional tickets have to be printed.

Find N and X?







Answer

Let before adding X stations, total number of tickets
t = N(N-1)
After adding X stations total number of tickets are
t + 46 = (N+X)(N+X-1)
Subtracting 1st from 2nd
46 = (N+X)(N+X-1) - N(N-1)
46 = N2 + NX - N + NX + X2 - X - N2 + N
46 = 2NX + X2 - X
46 = (2N - 1)X + X2
X2 + (2N - 1)X - 46 = 0

Now there are only two possible factors of 46. They are (46,1) and (23,2)
Case I: (46,1)
2N - 1 = 45
2N = 46
N = 23
 
And X = 1
 
Case II: (23,2)
2N - 1 = 21
2N = 22
N = 11
 
And X = 2
Hence, there are 2 possible answers.
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Saturday, January 26, 2013

Puzzles With Answers For Campus Placement - Part-9 | Infosys Puzzles With Answers- Part-12

1. A Lorry Starts From Banglore To Mysore At 6.00 Am, 7.00 Am, 8.00 Am.....10 Pm. Similarly on another side starts from Mysore to Banglore at 6.00 Am, 7.00 Am, 8.00 Am.....10.00 Pm. A Lorry Takes 9 Hours To Travel From Banglore To Mysore And Vice Versa.
(I) A Lorry Which Has Started At 6.00 Am Will Cross How Many Lorries.
Answer: 17.
(II) A Lorry Which Had Started At 6.00 Pm Will Cross How Many Lorries.
Answer: 13.

2. A Person Meets A Train At A Railway Station Coming Daily At A Particular Time . One Day He Is Late By 25 Minutes, And He Meets The Train 5 K.M. Before The Station. If His Speed Is 12 Kmph, What Is The Speed Of The Train.
Answer: 60 Kmph. Refer--Shakuntala Devi Book.

3. A Thief Steals Half the Total No of Loaves of Bread Plus 1/2 Loaf from A Bakery. A Second Thief Steals Half the Remaining No of Loaves Plus 1/2 Loaf And So On. After The 5th Thief Has Stolen There Are No More Loaves Left In The Bakery. What Was The Total No Of Loaves Did The Bakery Have At The Beginning.
Answer: 30.

5. From A Vessel, 1/3rd Of The Liquid Evaporates On The First Day. On The Second Day 3/4th Of The Remaining Liquid Evaporates. What Fraction Of The Volume Is Present At The End Of The Second Day.
Answer: 25%.

6. There Is A 4 Inch Cube Painted On All Sides. This Is Cut Down Into Of 1 Inch Cubes. What Is The No Of Cubes Which Have No Pointed Sides?
Answer: 8.

7. Sam And Mala Have A Conversation. Sam Says I Am Certainly Not Over 40. Mala Says I Am 38 And You Are Atleast 5 Years Older Than Me. Now, Sam Says You Are Atleast 39. All The Statements By The Two Are False. How Old Are They Really?
Answer: Mala = 38 Yrs; Sam = 41 Yrs.

8. In A Railway Station, There Are Two Trains Going. One in the Harbour Line and One in the Main Line, Each Having a Frequency of 10 Minutes. The Main Line Service Starts At 5 O'clock And The Harbour Line Starts At 5.02 AM A Man Goes To The Station Every Day To Catch The First Train That Comes. What Is The Probability Of The Man Catching The First Train?
Answer: 0.8.

9. A Family X Went For A Vacation. Unfortunately It Rained For 13 Days When They Were There. But Whenever It Rained In The Mornings, They Had Clear Afternoons And Vice Versa. In All They Enjoyed 11 Mornings And 12 Afternoons. How Many Days Did They Stay There Totally?
Answer: 23 Days.

10. Olympic Race: 4 Contestants: Alan, Charlie, Darren, And Brain. There Are Two Races And Average Is Taken To Decide The Winner. One Person Comes At The Same Position In Both The Race. Charlie Always Come Before Darren. Brian Comes First Once. Alan Comes Third Atleast Once. Find The Positions. Alan Never Comes Last. Charlie & Darren Comes 2nd Atleast Once.
Answer: Alan 3, 3; Charlie 1,2 ; Darren 2,4; Brain 1, 4;
So on Average the winners are as follows: 1-Charlie; 2-Brain; 3-Alan & Darren
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