Find Numbers For The Boxes

Find the correct number to fill in the boxes below.

These should be correct numbers!

Finding Correct Numbers For The Boxes

How boxes are placed?

Let's assume a, b, c and d are the correct numbers in the boxes.

So, 4 equations that we get are,

a + b = 8     .....(1)

c - d = 6     .....(2)

a + c = 13   .....(3)

b + d = 8    .....(4)

Subtracting (1) from (3) gives,

c - b =  5     .....(5)

Adding (2) to (4),

c + b = 14    .....(6)

Adding (5) and (6) gives,

2c = 19

c = 9.5

Putting c = 9.5 in (2),

9.5 - d = 6

Hence, d = 3.5

Putting d =3.5 in (4),

b + 3.5 = 8

b = 4.5

Putting b = 4.5 in (1),

a + 4.5 = 8

a = 3.5

So to conclude, a = 3.5, b = 4.5, c = 9.5 and d = 3.5.

Mathematical Talk Between Horse And Camel

A horse and a camel were carrying boxes on their backs. The horse started complaining to the camel that his load is too heavy.

The camel replied 'Why are you complaining? If you gave me one of your boxes I would have double what you have and if I give you one of my boxes we two would have an even load.'

How many boxes do each of the animal (horse & camel) is carrying ?

Find here the load on each of them! 
 

Suggestion From Mathematical Talk!

What was the talk?

Let's assume C be the number of boxes that camel is carrying and H be that being carried by horse.

As per first part of camel's statement i.e. if you gave me one of your boxes I would have double what you have  

C + 1 = 2 (H - 1) 

C + 1 = 2H -2

C = 2H - 3 ........(1)

Now in second part (i.e.if I give you one of my boxes we two would have an even load) of camel's statement suggests,

C - 1 = H + 1 


C = H + 2 

Putting (1) in above,

2H - 3 = H + 2

H = 5

Again putting this value in (1) gives,

C = 2*5 - 3 = 10 - 3 = 7 

C = 7. 

Horse is carrying 5 boxes and the camel is carrying 7 boxes.  

 

A Clever Trader At Checkpoints

Anabelle is a clever trader of rare artifacts. Each day she carries three boxes with each filled with thirty artifacts. The boxes can't hold more than that. She travels far of northern lands to sell these artifacts but on way, she comes across thirty checkpoints where she has to shed one of the artifact for each sack to the authorities for letting her pass.

How many artifacts will be left with her when she reaches her destination crossing all the check points ?  

How she managed to save some? Find here! 

Source
 

A Cleaver Trader's Deal At Checkpoints

What was the situation?

Without any work to brain if she travels as it is through all checkpoints then at the end nothing would be left with her. Because at each checkpoint she has to shed 3 artifacts so at 30 checkpoints she has to shed 3 x 30 = 90 artifacts if she gives artifact from each box. And she has only 90 artifacts.

As a clever trader, she starts shedding artifacts from one box at each checkpoint. At first 10 checkpoints, 1 box would be emptied & 30 artifacts paid at checkpoints.

For next 15 checkpoints, she sheds all artifacts from second box thereby paying 30 artifacts.

For final 5 checkpoints, now she has to shed only 5 artifacts from third box with 25 artifacts remaining in the box.

So 25 artifacts will be left with her when she reaches her destination crossing all the check points.