## There is a escalator and 2 persons move down it. A takes 50 steps and B takes 75 steps while the escalator is moving down. Given that the time taken by A to take 1 step is equal to time taken by B to take 3 steps. Find the no. of steps in the escalator while it is stationary.

If A takes 1 step in one second, then B takes 3 steps in one second. If A takes t1 seconds to take 50 steps, then B takes 150 steps in t1 seconds.

For B, to take 150 steps he requires t1 seconds,

then to take 75 steps he requires t1/2 seconds.

So now, s1=50, t1 = t1 & s2=75, t2=t1/2

ans= (s1*t2 ~ s2*t1) / (t1 ~ t2) which gives 100.

so 100 steps is the answer

## Jolly Jugs Problems ?

You are standing next to a well, and you have two jugs. One jug has a content of 3 liters and the other one has a content of 5 liters.
**
Question: **How can you get just 4 liters of water using only these two jugs?

**Solution 1:**

Fill the 5 liter jug. Then fill the 3 liter jug to the top with water from the 5 liter jug. Now you have 2 liters of water in the 5 liter jug. Dump out the 3 liter jug and pour what’s in the 5 liter jug into the 3 liter jug. Then refill the 5 liter jug, and fill up the 3 liter jug to the top. Since there were already 2 liters of water in the 3 liter jug, 1 liter is removed from the 5 liter jug, leaving 4 liters of water in the 5 liter jug.
**Solution 2: **

Fill the 3 liter jug and pour it into the 5 liter jug. Then refill the 3 liter jug and fill up the 5 liter jug to the top. Since there were already 3 liters of water in the 5 liter jug, 2 liters of water are removed from the 3 liter jug, leaving 1 liter of water in the 3 liter jug. Then dump out the 5 liter jug and pour what’s in the 3 liter jug into the 5 liter jug. Refill the 3 liter jug and pour it into the 5 liter jug. Now you have 4 liters of water in the 5 liter jug.

## Growing Water-Lily Problem ?

In the middle of a round pool lies a beautiful water-lily. The water-lily doubles in size every day. After exactly 20 days the complete pool will be covered by the lily.

**Question:** After how many days will half of the pool be covered by the water-lily?
**
Solution:**Because the water-lily doubles its size every day and the complete pool is covered after 20 days, half of the pool will be covered one day before that, after 19 days.

Conclusion: After 19 days half of the pool will be covered by the water-lily

## The Wolf, the Goat, and the Cabbage Problem ?

A man has a wolf, a goat, and a cabbage. He must cross a river with the two animals and the cabbage. There is a small rowing-boat, in which he can take only one thing with him at a time. If, however, the wolf and the goat are left alone, the wolf will eat the goat. If the goat and the cabbage are left alone, the goat will eat the cabbage.

**Question:** How can the man get across the river with the two animals and the cabbage?

**Solution:**

First, the man takes the goat across, leaving the wolf with the cabbage. Then he goes back. Next, he takes the wolf across. Then the man goes back, taking the goat with him. After this, he takes the cabbage across. Then he goes back again, leaving the wolf with the cabbage. Finally, he takes the goat across.

First, the man takes the goat across, leaving the wolf with the cabbage. Then he goes back. Next, he takes the cabbage across. Then the man goes back, taking the goat with him. After this, he takes the wolf across. Then he goes back again, leaving the wolf with the cabbage. Finally, he takes the goat across.

## Happy Handshaking Problem?

Jack and his wife went to a party where four other married couples were present. Every person shook hands with everyone he or she was not acquainted with. When the handshaking was over, Jack asked everyone, including his own wife, how many hands they shook. To his surprise, Jack got nine different answers.

**Question:** How many hands did Jack’s wife shake?

**Solution:** Because, obviously, no person shook hands with his or her partner, nobody shook hands with more than eight other people. And since nine people shook hands with different numbers of people, these numbers must be 0, 1, 2, 3, 4, 5, 6, 7, and 8.

The person who shook 8 hands only did not shake hands with his or her partner, and must therefore be married to the person who shook 0 hands.

The person who shook 7 hands, shook hands with all people who also shook hands with the person who shook 8 hands (so in total at least 2 handshakes per person), except for his or her partner. So this person must be married to the person who shook 1 hand.

The person who shook 6 hands, shook hands with all people who also shook hands with the persons who shook 8 and 7 hands (so in total at least 3 handshakes per person), except for his or her partner. So this person must be married to the person who shook 2 hands.

The person who shook 5 hands, shook hands with all people who also shook hands with the persons who shook 8, 7, and 6 hands (so in total at least 4 handshakes per person), except for his or her partner. So this person must be married to the person who shook 3 hands.

The only person left, is the one who shook 4 hands, and which must be Jack’s wife. The answer is: Jack’s wife shook 4 hands

## The Round Table Problem ?

Yesterday evening, Helen and her husband invited their neighbours (two couples) for a dinner at home. The six of them sat at a round table. Helen tells you the following: “Victor sat on the left of the woman who sat on the left of the man who sat on the left of Anna. Esther sat on the left of the man who sat on the left of the woman who sat on the left of the man who sat on the left of the woman who sat on the left of my husband. Jim sat on the left of the woman who sat on the left of Roger. I did not sit beside my husband.” The

**Question:** What is the name of Helen’s husband?

**Solution:**From the second statement, we know that the six people sat at the table in the following way (clockwise and starting with

Helen’s husband): Helen’s husband, woman, man, woman, man, Esther

Because Helen did not sit beside her husband, the situation must be as follows: Helen’s husband, woman, man, Helen, man, Esther

The remaining woman must be Anna, and combining this with the first statement, we arrive at the following situation: Helen’s husband, Anna, man, Helen, Victor, Esther

Because of the third statement, Jim and Roger can be placed in only one way, and we now know the complete order: Helen’s husband Roger, Anna, Jim, Helen, Victor, Esther

Conclusion: the name of Helen’s husband is Roger.

**Three years back the age of a father was 24 years more than his son. At present the father is 5 times as old as the son. How old will the son be three years from now?**

f-3=24+s

f=5s

5s=27+s

s=27/4

s+3 = 27/4 + 12/4 = 39/4

f-3=24+s

f=5s

5s=21+s

s=21/4

s+3 = 27/4 + 12/4 = 39/4

9.75

**A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 40 seconds. What is the length of the train in meters?**

1777 meters | | (2) | 1822 meters | |

(3) | 400 meters | | (4) | 400 meters |

**Correct choice - (3) Correct Answer -(400 meters)**

**Explanatory Answer**

**Note**

When a train overtakes another object such as a motorbike, whose length is negligible compared to the length of the train, then the distance traveled by the train while overtaking the motorbike is the same as the length of the train.

The length of the train = distance traveled by the train while overtaking the motorbike

= relative speed between the train and the motorbike * time taken

In this case, as both the objects i.e., the train and the motorbike are moving in the same direction, the relative speed between them = difference between their respective speeds = 100 - 64 = 36 kmph.

Distance traveled by the train while overtaking the motorbike = 36 kmph * 40 seconds.

The final answer is given in meters and the speed is given in kmph and the time in seconds.

So let us convert the given speed from kmph to m/sec.

1 kmph = 5/18 m/sec

Therefore, 36 kmph = 36 * 5 /18 = 10 m/sec.

Relative speed = 10 m/sec. Time taken = 40 seconds.

Therefore, distance traveled = 10 * 40 = 400 meters.

**Steve traveled the first 2 hours of his journey at 40 mph and the remaining 3 hours of his journey at 80 mph. What is his average speed for the entire journey?**

a. 56.67 mph c. 60 mph

b. 66.67 mph d. 64 mph e. 53.33 mph

AVG SPEED = (2X40)+(3X80)/5 =64

**By selling an article at 80% of its marked price, a merchant makes a loss of 12%. What will be the % profit made by the merchant if he sells the article at 95% of its marked price?**

a. 4.5% profit \ c. 5.5% profit

b. 10% profit d. 5% profit e. 1% loss

SUPPOSE COST=100

MARKET PRICE=M

80% M= (100-12)

80M/100=88

M= 88*100/80

M=110

CURRENT SELLING PRICE =110*95/100

=104.5

PROFIT= 104.5-100=4.5

% =4.5/100*100 =4.5

4. Select the antonym of capture from the following

a. attack c. condemn

b. Release d. None of the above

ANSW: RELEASE

**The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number?**

a. 60 c. 40

b. 120 d. 160 e. 80

=(X+12.5X/100) –(X- 25X/100)=30

(112.5X-75X)/100=30

37.5 X =3000

X =3000/37.5= 80

**The wages earned by Robin is 30% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much % is the wages earned by Charles more than that earned by Robin?**

a. 100% c. 30%

b. 18.75% d. 50% e. 23%

ROBIN= (E+30E/100); E=ERICA

CHARLES= (E+60E/100)

ROBIN= 130E

CHARLES =160E

SO %= (160E-130E/130E)

(=30/130)*100

=23

**What is the maximum percentage discount that a merchant can offer on her Marked Price so that she ends up selling at no profit or loss, if she had initially marked her goods up by 50%?**

a. 33.33% c. 20%

b. 16.67% d. 25% e. 50%** **

SUPPOSE COST=100

SELLING PRICE= 150

MAX DISCOUNT AT WHICH NO PROFIT NO LOSS

= RS 50

% = (50/150*100)

=33.33

More Puzzles : http://www.freepuzzles.com/

**Courtesy : Alan Bibin, IIM B, ****Bangalore**** **

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