Viral Maths Problem Confusing Students & Parents

There are 73 red, blue and green marbles in a jar. There are twice as many red marbles as blue marbles. There are 19 more marbles than green marbles. 

How many green marbles are there?

Check if you are correct! 

Solution of Viral Maths Problem Confusing Students & Parents

What was the problem?

Using Algebra : 

Let r,b and g be the numbers of red, blue and green marbles in the jar.

There are 73 red, blue and green marbles in a jar.

So r + b + g = 73    .....(1)

There are twice as many red marbles as blue marbles.

r = 2b                  ......(2)

There are 19 more blue marbles than green marbles. 

b = g + 19            

g = b - 19            ......(3)

Putting (2) and (3) in (1), gives

2b + b + b - 19 = 73

4b = 92

b = 23

Putting b = 23 in (3) gives,

g = 23 - 19 = 4

Putting  b = 23 in (2), gives 

r = 2x23 = 46

So there are 46 red,23 blue and 4 green marbles in the jar.

Without Algebra :

In the case, we need to try trail and error method.

If g = 1, then b = 20 and r = 2(20) = 40 giving total 40 + 20 + 1 = 61.

If g = 2, then b = 21 and r = 2(21) = 42 giving total 42 + 21 + 2 = 65.

If g = 3, then b = 22 and r = 2(22) = 44 giving total 44 + 22 + 3 = 69.

Total is increasing at the rate of 4. So finally,

If g = 4, then b = 23 and r = 2(23) = 46 giving total 46 + 23 + 4 = 73.


So there are 46 red,23 blue and 4 green marbles in the jar.

100m Running Race

Lavesh, Bolt, and Lewis race each other in a 100 meters race. All of them run at a constant speed throughout the race.

Lavesh beats Bolt by 20 meters.
Bolt beats Lewis by 20 meters.

How many meters does Lavesh beat Lewis by ? 

Know here the answer! 

Source 

Winner Beats Second Runner Up by...

What was the question? 

Let Lavesh's speed be 10 m/s. Then he must have taken 10 seconds to finish the race. Since Bolt was beaten by Lavesh by 20 m he must have run 80m when Lavesh finished race in 10 seconds (t=10). So his speed would be 8 m/s.

Now Bolt requires 100/0.8 = 12.5 seconds to finish the race. When he finished, Lewis was 20m behind i.e. 80m from starting point at t = 12.5. So Lewis speed is 80/12.5 = 6.4 m/s

At t = 10 seconds, when Lavesh finished his race Lewis must be at 6.4 x 10 = 64 m from starting point. Hence Lavesh beats Lewis by 100 - 64 = 36 m.

Another method.

Let L be the speed of Lavesh, B be the speed of Bolt & W be that of Lewis. Then,

L/B = 100/80 = 5/4

L = (5/4) B  .......(1)

Similarly,

B/W = 100/80 = 5/4

B = (5/4) W .......(2)

Putting (2) into (1),

L = (5/4) x (5/4) W

L/W = 25/16

L = (25/16) W

For given time t, when Lavesh finished the race,

Distance by L/ Distance by W = 25 / 16

100 m/ Distance by W = 25 / 16

Distance by W = (16 x 100) / 25 = 64.

  
So when Lavesh finished cross line at 100 m, Lewis was at 64m i.e. 36m behind. In other words, Lavesh beats Lewis by 100 - 64 = 36 m.

Test Of Poison

You are the ruler of a medieval empire and you are about to have a celebration tomorrow. The celebration is the most important party you have ever hosted. You've got 1000 bottles of wine you were planning to open for the celebration, but you find out that one of them is poisoned.

The poison exhibits no symptoms until death. Death occurs within ten to twenty hours after consuming even the minutest amount of poison.

You have over a thousand slaves at your disposal and just under 24 hours to determine which single bottle is poisoned.

You have a handful of prisoners about to be executed, and it would mar your celebration to have anyone else killed.

What is the smallest number of prisoners you must have to drink from the bottles to be absolutely sure to find the poisoned bottle within 24 hours? 

Here is the test designed for it! 

Source 

Test To Detect The Poison

Here is the challenge for us! 

Here binary number system can come to rescue. Just for a  moment, let's assume there are 15 bottles. Now let's number the bottles from 1 to 15. To test these 15 bottles we need 4 prisoners as below. Let's number the prisoners from in descending 4 to 1.

Wherever 1 is written for the particular bottle number, that bottle should be given to particular prisoner. Otherwise should not.

So for the specific bottle with unique number a specific combination of prisoners (they are bits here) would be formed. 

For example, if bottle labeled as 11 has a poison then prisoner no. 4,2,1 would die. In other words, if prisoner 4 & 2 die then the bottle no. 10 had poison.

For 16th bottle we would have needed 1 more prisoner.

In similar way, to test 1000 bottles, we need 10 prisoners (2^10=1024). Depending on what combination of prisoner die we can determine which bottle had poison. If prisoners numbered from 10 to 1 & if prisoner 10,8,6,3 & 2 die then bottle no.678 (binary - 1010100110) must had poison. Since the poison takes some time to take effect, even if prisoners taste this bottle, we still would have time to test rest of all bottles in given binary pattern. 

  Poisonous Bottle

In case there were 1025 bottle, we would have needed 11 prisoners.

 

How Many Animals Are Going Towards River?

One rabbit saw 6 elephants while going towards river.

Every elephant saw 2 monkeys are going towards river.

Every monkey holds one parrot in their hands.

Now tell me how many animals are going towards river.

How Many I Saw

How many? Click here! 

There Are Total....Animals Going Towards The River!

What was the question? 

One thing is sure 1 rabbit is definitely going towards the river. And parrot is definitely not an animal; it's a bird.

Now there are 2 possibilities.

1. Every elephant saw 2 different monkeys then there are total 12 monkeys & 1 rabbit going towards river. So total 13 animals moving towards river.

2. Every elephant saw same 2 monkeys then there are total 2 monkeys & 1 rabbit going towards river. So total 3 animals moving towards river.

Actually I saw...

The Shopping Challenge

At a stationary shop, shopkeeper sells notebook at Rs.15, Pen at Rs.1 & Eraser at Rs.0.25. You are asked to purchase 100 objects & you are given Rs.100 note. 

So how many notebooks,pens & erasers would you buy?

Shopping Challenge

Here is what should you do! 

Taking The Shopping Challenge

What was the problem?

Let N = number of notebooks, P = number of pens & E = number of erasers.

From the given maths we get 2 equations as,

N + P + E = 100................(1)

15N +1P +E/4=100…....(2)
 
From (1),

P = 100 - N - E

From (2),

60N + 4P + E= 400

60N + 4(100-N-E) + E = 400

60N + 400-4N-4E + E = 400

56N - 3E = 0

56N = 3E

N/E = 3/56

From the ratio, we get, N=3, E=56.

Putting these in equation (1),

We get,

P=41.

So we should buy 56 erasers,41 pens & 3 notebooks to satisfy the given condition. 

Unfair Loss in Savings of Life

On his 20th birthday, Ajay started depositing Rs.500 in his saving box. His brother Vijay used to withdraw Rs.100 from the same box on his birthday every year. On his 60th  birthday, Ajay opens his box & finds only Rs.1000 in it.

How this could be possible?

Ajay & Vijay

This is how it's possible 

Having Birthday On Leap Day

What was looking impossible?

Since Ajay celebrates his birthday on 29th February, he used to deposit Rs.500 in saving box once in 4 years. From age 20 to 60, he celebrated only 10 birthdays saving only 500 x 10 = 5000. 

But Vijay withdrawing Rs.100 every year means he took 100 x 40 = 4000 so far.

That's why only 5000 - 4000 = 1000 left in the box.

Would You Help This Farmer ?

A farmer had 25 cows. To identify easily he numbered them from 1 to 25. Interestingly, each cow produces liters of milk equal to the respective number given. For example, a cow numbered 5 gives 5 liters of milk or a cow numbered 18 produces 18 liters of milk. Now that farmer had 5 sons. Farmer wants to share those 25 cows among his 5 sons with each son getting 5 cows. But he wants to make sure each son would get equal amount of milk.

How should he make 5 groups of cows to distribute among his sons?

Please, Help me!

This is what farmer need to do! 

Fair Distribution of Farmer's Cows

What was the interesting?

First let's name 5 sons as A,B,C,D & E. Now look at the image below.

Just collect numbers surrounded by same shapes. If you observe carefully answer, a difference of 4 created at one place which is compensated at other 4. Each son would be getting 65 liters of milk.

Fair Distribution of Cows