PUZZLE 3

PUZZLE 3

1) 1/3 rd of the contents of a container evaporated on the 1st day. 3/4th of the remaining contents of the container evaporated on the second day. What part of the contents of the container is left at the end of the second day?

2) Vipul was studying for his examinations and the lights went off. It was around 1:00 AM. He lighted two uniform candles of equal length but one thicker than the other. The thick candle is supposed to last six hours and the thin one two hours less. When he finally went to sleep, the thick candle was twice as long as the thin one.

For how long did Vipul study in candle light?

3) If you started a business in which you earned Rs.1 on the first day, Rs.3 on the second day, Rs.5 on the third day, Rs.7 on the fourth day, & so on.

How much would you have earned with this business after 50 years (assuming there are exactly 365 days in every year)?

Math gurus may use series formula to solve it.(series: 1,3,5,7,9,11.....upto 18250 terms)

4) A worker earns a 5% raise. A year later, the worker receives a 2.5% cut in pay, & now his salary is Rs. 22702.68

What was his salary to begin with?

5) At 6'o a clock ticks 6 times. The time between first and last ticks is 30 seconds. How long does it tick at 12'o.

6) In Mr. Mehta's family, there are one grandfather, one grandmother, two fathers, two mothers, one father-in-law, one mother-in-law, four children, three grandchildren, one brother, two sisters, two sons, two daughters and one daughter-in-law. How many members are there in Mr. Mehta's family? Give minimal possible answer.

7) When Alexander the Great attacked the forces of Porus, an Indian soldier was captured by the Greeks. He had displayed such bravery in battle, however, that the enemy offered to let him choose how he wanted to be killed. They told him, "If you tell a lie, you will put to the sword, and if you tell the truth you will be hanged."

The soldier could make only one statement. He made that statement and went free. What did he say?

8) A person wanted to withdraw X rupees and Y paise from the bank. But cashier made a mistake and gave him Y rupees and X paise. Neither the person nor the cashier noticed that.

After spending 20 paise, the person counts the money. And to his surprise, he has double the amount he wanted to withdraw.

Find X and Y. (1 Rupee = 100 Paise)

9) At the Party:

There were 9 men and children.

There were 2 more women than children.

The number of different man-woman couples possible was 24. Note that if there were 7 men and 5 women, then there would have been 35 man-woman couples possible.

Also, of the three groups - men, women and children - at the party:

There were 4 of one group.

There were 6 of one group.

There were 8 of one group.

Exactly one of the above 6 statements is false.

Can you tell which one is false? Also, how many men, women and children are there at the party

10) There is a shortage of tube lights , bulbs and fans in a village - Kharghar. It is found that

All houses do not have either tubelight or bulb or fan.

exactly 19% of houses do not have just one of these.

atleast 67% of houses do not have tubelights.

atleast 83% of houses do not have bulbs.

atleast 73% of houses do not have fans.

What percentage of houses do not have tubelight, bulb and fan?

11) Mr. Subramaniam rents a private car for Andheri-Colaba-Andheri trip. It costs him Rs. 300 everyday.

One day the car driver informed Mr. Subramaniam that there were two students from Bandra who wished to go from Bandra to Colaba and back to Bandra. Bandra is halfway between Andheri and Colaba. Mr. Subramaniam asked the driver to let the students travel with him.

On the first day when they came, Mr. Subramaniam said, "If you tell me the mathematically correct price you should pay individually for your portion of the trip, I will let you travel for free."

How much should the individual student pay for their journey?

12) In training for a competition, you find that swimming downstream (with the current) in a river, you can swim 2 miles in 40 minutes, & upstream (against the current), you can swim 2 miles in 60 minutes.

How long would it take you to swim a mile in still water?

13) How many different ways can this be accomplished? Note that the first person can choose any of the 11 seats.

(question is not completly avilable..will be updated asap)

14) The ratio of Boys to Girls is 6:4. 60% of the boys and 40% of the girls take lunch in the canteen. What % of class takes lunch in canteen?

15) In the General meeting of "Friends Club", Sameer said, "The repairs to the Club will come to a total of Rs 3120 and I propose that this amount should be met by the members, each paying an equal amount."

The proposal was immediately agreed. However, four members of the Club chose to resign, leaving the remaining members to pay an extra Rs 26 each.

How many members did the Club originally have?

16) A tank can be filled by pipe A in 30 minutes and by pipe B in 24 minutes. Outlet pipe C can empty the full tank in one hour and twenty minutes.

If the tank is empty initially and if all the three pipes A, B and C are opened simultaneously, in how much time will the tank be full?

17) A rich old Arab has three sons. When he died, he willed his 17 camels to the sons, to be divided as follows:

First Son to get 1/2 of the camels Second Son to get 1/3rd of the camels Third Son to get 1/9th of the camels.

The sons are sitting there trying to figure out how this can possibly be done, when a very old wise man goes riding by. They stop him and ask him to help them solve their problem. Without hesitation he divides the camels properly and continues riding on his way.

How did he do it?

18) There are 3 colored boxes - Red, Green and Blue. Each box contains 2 envelopes. Each envelope contains money - two of them contain Rs. 25000 each, two of them contain Rs. 15000 each and remaining two contain Rs. 10000 each.

There is one statement written on the cover of each box.

* Red Box: Both, a red box and a blue box contain Rs. 10000 each.

* Green Box: Both, a green box and a red box contain Rs. 25000 each.

* Blue Box: Both, a blue box and a green box contain Rs. 15000 each.

Only one of the above 3 statements is true and the corresponding box contains the maximum amount.

Can you tell which box contains the maximum amount and how much?

19) Sachin, Dravid and Ganguly played in a Cricket match between India and England.

None of them scored more than 99 runs.

If you add the digits of the runs scored by Sachin to his own score, you will get the runs scored by Dravid.

If you reverse the digits of the runs scored by Dravid, you will get the runs scored by Ganguly.

The total runs scored by them is 240.

Can you figure out their individual scores?

20) Substitute digits for the letters to make the following relation true.

W O R L D

+ T R A D E

C E N T E R

Note that the leftmost letter can't be zero in any word. Also, there must be a one-to-one mapping between digits and letters. e.g. if you substitute 3 for the letter W, no other letter can be 3 and all other W in the puzzle must be 3.

PUZZLE 3 Answers

1)Assume that contents of the container is X

On the first day 1/3rd is evaporated.

(1 - 1/3) of X is remaining i.e. (2/3)X

On the Second day 3/4th is evaporated. Hence,

(1- 3/4) of (2/3)X is remaining

i.e. (1/4)(2/3)X = (1/6) X

Hence 1/6th of the contents of the container is remaining

2)

Vipul studied for 3 hours in candle light.

Assume that the initial lenght of both the candle was L and Vipul studied for X hours.

In X hours, total thick candle burnt = XL/6

In X hours, total thin candle burnt = XL/4

After X hours, total thick candle remaining = L - XL/6

After X hours, total thin candle remaining = L - XL/4

Also, it is given that the thick candle was twice as long as the thin one when he finally went to sleep.

(L - XL/6) = 2(L - XL/4)

(6 - X)/6 = (4 - X)/2

(6 - X) = 3*(4 - X)

6 - X = 12 - 3X

2X = 6

X = 3

Hence, Vipul studied for 3 hours i.e. 180 minutes in candle light.

3)

Rs.333,062,500

To begin with, you want to know the total number of days: 365 x 50 = 18250.

By experimentation, the following formula can be discovered, & used to determine the amount earned for any particular day: 1 + 2(x-1), with x being the number of the day. Take half of the 18250 days, & pair them up with the other half in the following way: day 1 with day 18250, day 2 with day 18249, & so on, & you will see that if you add these pairs together, they always equal Rs.36500.

Multiply this number by the total number of pairs (9125), & you have the amount you would have earned in 50 years.

4)

Rs.22176

Assume his salary was Rs. X

He earns 5% raise. So his salary is (105*X)/100

A year later he receives 2.5% cut. So his salary is ((105*X)/100)*(97.5/100) which is Rs. 22702.68

Hence, solving equation ((105*X)/100)*(97.5/100) = 22702.68

X = 22176

5)

66 seconds

It is given that the time between first and last ticks at 6'o is 30 seconds.

Total time gaps between first and last ticks at 6'o = 5

(i.e. between 1 & 2, 2 & 3, 3 & 4, 4 & 5 and 5 & 6)

So time gap between two ticks = 30/5 = 6 seconds.

Now, total time gaps between first and last ticks at 12'o = 11

Therefore time taken for 12 ticks = 11 * 6 = 66 seconds (and not 60 seconds)

6)

There are 7 members in Mr. Mehta's family. Mother & Father of Mr. Mehta, Mr. & Mrs. Mehta, his son and two daughters.

Mother & Father of Mr. Mehta

|

Mr. & Mrs. Mehta

|

One Son & Two Daughters

7)

The soldier said, "You will put me to the sword."

The soldier has to say a Paradox to save himself. If his statement is true, he will be hanged, which is not the sword and hence false. If his statement is false, he will be put to the sword, which will make it true. A Paradox !!!

8)

As given, the person wanted to withdraw 100X + Y paise.

But he got 100Y + X paise.

After spending 20 paise, he has double the amount he wanted to withdraw. Hence, the equation is

2 * (100X + Y) = 100Y + X - 20

200X + 2Y = 100Y +X - 20

199X - 98Y = -20

98Y - 199X = 20

Now, we got one equation; but there are 2 variables. We have to apply little bit of logic over here. We know that if we interchange X & Y, amount gets double. So Y should be twice of X or one more than twice of X i.e. Y = 2X or Y = 2X+1

Case I : Y=2X

Solving two equations simultaneously

98Y - 199X = 20

Y - 2X = 0

We get X = - 20/3 & Y = - 40/2

Case II : Y=2X+1

Solving two equations simultaneously

98Y - 199X = 20

Y - 2X = 1

We get X = 26 & Y = 53

Now, its obvious that he wanted to withdraw Rs. 26.53

9)

Statement (4) is false. There are 3 men, 8 women and 6 children.

Assume that Statements (4), (5) and (6) are all true. Then, Statement (1) is false. But then Statement (2) and (3) both can not be true. Thus, contradictory to the fact that exactly one statement is false.

So Statement (4) or Statement (5) or Statement (6) is false. Also, Statements (1), (2) and (3) all are true.

From (1) and (2), there are 11 men and women. Then from (3), there are 2 possible cases - either there are 8 men and 3 women or there are 3 men and 8 women.

If there are 8 men and 3 women, then there is 1 child. Then Statements (4) and (5) both are false, which is not possible.

Hence, there are 3 men, 8 women and 6 children. Statement (4) is false.

10)

42% houses do not have tubelight, bulb and fan.

Let's assume that there are 100 houses. Hence, there should be total 300 items i.e. 100 tubelights, 100 bulbs and 100 fans.

From the given data, we know that there is shortage of atleast (67+83+73) 223 items in every 100 houses.

Also, exactly 19 houses do not have just one item. It means that remaining 81 houses should account for the shortage of remaining (223-19) 204 items. If those remaining 81 houses do not have 2 items each, there would be a shortage of 162 items. But total of 204 items are short. Hence, atleast (204-162) 42 houses do not have all 3 items - tubelight, bulb and fan.

Thus, 42% houses do not have tubelight, bulb and fan.

11)

The individual student should pay Rs. 50 for their journey.

Note that 3 persons are travelling between Bandra and Colaba.

The entire trip costs Rs. 300 to Mr. Subramanian. Hence, half of the trip costs Rs. 150.

For Andheri-Bandra-Andheri, only one person i.e. Mr. Subramaniam is travelling. Hence, he would pay Rs. 150.

For Bandra-Colaba-Bandra, three persons i.e Mr. Subramaniam and two students, are travelling. Hence, each student would pay Rs. 50.

12)

You are able to swim downstream at 3 miles an hour, & upstream at 2 miles an hour. There is a difference of 1 mile an hour, which is the river helping you in 1 direction, & slowing you in the other direction.

Average the 2 rates, & you have the rate that you can swim in still water, which is 2.5 miles an hour.

You can thus swim a mile in still water in 24 minutes.

13)

There are 1024 different ways.

This is the type of Brain Teaser that can be solved using the method of induction.

If there is just a one person and one seat, that person has only one option.

If there are two persons and two seats, it can be accomplished in 2 different ways.

If there are three persons and three seats, it can be accomplished in 4 different ways. Remember that no person can take a seat that separates him/her from at least one other person.

Similarly, four persons and four seats produce 8 different ways. And five persons with five seats produce 16 different ways.

It can be seen that with each additional person and seat, the different ways increase by the power of two. For six persons with six seats, there are 32 different ways.

For any number N, the different possible ways are 2 ^ (N-1)

Thus, for 11 persons and 11 seats, total different ways are 2 ^ 10 i.e. 1024

14)

Assume there are 6X boys and 4X Girls

Total Students taking lunch in canteen

= (6X)(60/100) + (4X)(40/100)

= 36(X/10) + 16(X/10)

= 52(X/10)

Total students are = 6X + 4X = 10X

% of class taking lunch in canteen

= ((52X/10) * 100 ) / 10X

= 52 %

15)

The Club originally had 24 members.

Assume that there were initially N members.

As 4 members resigned and remaining members paid Rs 26 each, it means that total amount of 4 members is equal to Rs 26 each from remaining (N-4) members. Thus,

4 * (3120 / N) = 26 * (N - 4)

12480 = 26N2 - 104N

26N2 - 104N - 12480 = 0

Solving the quadratic equation we get N=24.

Hence, the Club originally had 24 members.

16)

The tank will be full in 16 minutes.

In one minute,

pipe A can fill 1/30 part of the tank.

pipe B can fill 1/24 part of the tank.

pipe C can empty 1/80 part of the tank.

Thus, the net water level in one minute is

= 1/30 + 1/24 - 1/80

= 15/240 part of the tank

Hence, the tank will be full in 240/15 i.e. 16 minutes.

17)

The old man temporarily added his camel to the 17, making a total of 18 camels.

First son got 1/2 of it = 9

Second son got 1/3 of it = 6

Third son got 1/9 of it = 2

For a total of 17. He then takes his camel back and rides away......

18)

Blue box contains the maximum amount Rs. 40000

As it is given that only one of the given 3 statements is true; assume in turn, each statement to be true & the other 2 false and check whether the corresponding box contains the maximum amount.

Let's assume that the statement on the Blue box is true. Thus, the given 3 statements can be interpreted as

* Atmost one, a red box or a blue box contains Rs. 10000.

* Atmost one, a green box or a red box contains Rs. 25000.

* Both, a blue box and a green box contain Rs. 15000 each.

Going through all possible combinations, we can conclude that

Red Box : Rs. 10000 + Rs. 25000 = Rs. 35000

Green Box : Rs. 10000 + Rs. 15000 = Rs. 25000

Blue Box : Rs. 15000 + Rs. 25000 = Rs. 40000

You can test out for other two statements i.e. assuming Red box statement true and then Green box statement true. In both the cases, other statements will contradict the true statement.

19)

achin, Dravid and Ganguly scored 75, 87 and 78 respectively.

Sachin's score must be less than 86, otherwise Dravid's score would be more than 99. Also, he must have scored atleast 42 - incase Dravid and Ganguly scored 99 each.

Also, as none of them scored more than 99 and the total runs scored by them is 240; their individual scores must be around 80.

20)

A tough one.

It is obvious that C=1. Also, the maximum possible value of E is 7. Now, start putting possible values of D, E and R as they occure frequently and use trial-n-error.

W O R L D 5 3 6 8 4

+ T R A D E + 7 6 0 4 2

C E N T E R 1 2 9 7 2 6