Similarly the Second Tribesman Said That the Third Was a 'Jhuta'

Qus301

In an isolated island lived two tribes: SACHAS and JHUTAS. The Sachas always speak the truth and the Jhutas never do.

One day a stranger on the island met four tribesmen and he asked one of them whether the second was a Sacha or Jhuta. Reply - 'Jhuta'.

Similarly the second tribesman said that the third was a 'Jhuta'.

The third tribesman said that the fourth was a ‘Jhuta’.

He asked the fourth tribesman what will the first tribesman have say about the third the reply was once again – ‘Jhuta’.

Who is who?

Ans.301

The first and third tribesman were Sachas and the other two were Jhutas.

Analysis:

If the question, ‘Are you a Sacha or a Jhuta’ is asked to a tribesman of that island the answer will always be ‘Sacha’ irrespective of the tribe he belongs to, because if he was a Sacha he has to speak the truth and if he were a Jhuta he will have to lie.

Also if two tribesman A & B belong to the same tribe (either Sachas or Jhutas) and the question,” Is B a Sacha or a Jhuta?’ is thrown at A the reply will always be Sacha. If they belong to different tribes the answer will always be, ‘Jhuta’.

As the first tribesman said that the second was a Jhuta we know that these are from different tribes.

With the same logic we can say that the second and the third tribesman were from different tribes.

So we now know that the first and third belong to the same tribe and the second belonged to the other.

Also the third and fourth tribesmen were from different tribes.

So the first and third were Jhutas and second and fourth were Sachas or vice versa.

Now if the first tribesman is asked whether the third was a Sacha or Jhuta should have replied ‘Sacha’ as both were from the same tribe, so the fourth tribesman according to whom the reply of the first should have been to the contrary, MUST BE A JHUTA.

Ques302

HEERALAL, a shrewd businessman made the following proposal on New Year’s eve to JHORILAL:

Everyday I will give you $500,000/-.

In return you pay me one cent on the first day of the month, two on the second, four on the third, eight on the forth day and so on for a month.

If it is all right with you we can start tomorrow.

JOHARILAL declined.

Why?

Ans.302

In case JHORILAL accepts the deal he would get $15,500,000/- from HIRALAL in the 31 days in January.

JOHARILAL would have to pay:

$ 5.26 on the tenth day.

$ 5,242.88 on the twentieth day.

$ 167,772.16 on the twenty-fifth day.

$ 1,342,177.28 on the twenty-eighth day.

$ 10,737,418.24 on the last day.

A staggering total of $ 21,474,836.47 for the month of January.

Ques.303

You are given twenty-seven balls; one of them being heavier than the others whose weights is the same.

In three weighing (by using a balancing scale) can the heavy ball be found out? An electronic or spring balance will require six weighing.

Ans.303

1st. Weighing:

Divide the balls into three groups of 9 balls each.

Weigh any two groups against each other.

If the scales balance the heavy one is in the third group if they don’t then pick up the heavy group of nine.

2nd. Weighing:

Divide the group of nine balls into three sub groups of three each and like the first weighing we can get the sub group of three with the heavy ball

3rd. Weighing:

Take any two balls and balance them against each other if the balance out then the one left out is the heaviest. If they do not balance out pick up the heavy one.

Ques.304

On a pasture the grass grows at an even rate.

40 cows can graze on it for 40 days and 30 cows can graze on it for 60 days before the grass is exhausted.

How many days can 20 cows graze on the pasture before the grass is exhausted?

Ans.304

The pasture would last 120 days if 20 cows were to graze on it.

Analysis:

In 40 days the pasture provides 1600 (40 X 40) feeds and in 60 days 1800 feeds (60 X 30).

So 20 days growth of grass allows for 200 feeds. (1800 - 1600).

Or the pasture grows enough grass to feed 10 cows every day.

So the before the cows start grazing the pasture has {1600-(40x10)} or {1800-(60x10)} feeds. Both work out to 1200 feeds.

Daily growth is adequate for feeding 10 cows endlessly.

So out of 20 cows the extra 10 will take 120 days to eat up the 1200 feeds existing on the pasture.

Ques.305

A ROPE WINDER, who, in school had learnt that the earth is round, worked all his life to make a rope long enough to go around the earth at the equator.

When he finally laid it along the Equator and pulled the ends tight, he found that the rope was a yard too long. (1 yard = 36 inches.)

Thinking that one-yard out of millions would be insignificant; he joined the two ends.

Assuming that the rope was stiff enough to make a self-standing circle of its own, how far will the rope be hovering over the earth?

Ans.305

SIX INCHES!

Analysis:

Let C be the circumference and R the radius of the earth at the equator.

So C = 2 II R

If r is the distance at which the rope hovers over the earth all around the Equator then:

C + 1 yard = 2 II (R + r)

So 1 yard = 2 II r which makes r approximately one sixth of yard which is 6 inches.