Solve the following equations and find the value of abc?

 

Let that something be 'x'

From the given data,

x + x/5 = 21

5x + x/5 = 21

6x = 21 x 5

=> x = 17.5

Hence, that something is x = 17.5.

In the given puzzle, the logic is the product of the number and its preceeding number gives the result.

9 = 9 x 8 = 72

8 = 8 x 7 = 56

7 = 7 x 6 = 42

6 = 6 x 5 = 30

5 = 5 x 4 = 20

Similarly,

3 = 3 x 2 = 6.

Here in the given puzzle,

2 x (2 + 2) = 8

3 x (3 + 3) = 18

4 x (4 + 4) = 32

5 x (5 + 5) = 50

Similarly,

6 x (6 + 6) = 72.

Here by observing the figure, 

we can complete the above incomplete cube with 2 cubes in 2 rows and 2 columns

=> 2 x 4 = 8.

Hence, with 8 small cubes we can complete the cube.

How many times can you subtract 10 from 100, for this if we go through logically, it is only 1 time. For the first time if we subtract 10 from 100, then there will no 100 to subtract from.

Hence, it is only 1 time we can subtract 10 from 100.

From the assumption and trial and error method,

last three digits sum must leave the same digit as the answer. It is possible only if the answer must be units digit number leaving tens digit as carry.

And the possible 3rd digit is 5. Since 5 + 5 + 5 = 15 

Now, 2nd step is  1 + x + x + x = 5

=> 3x = 4

It is possible with x = 8. 8 + 8 + 8 + 1 = 25 leaving 2 as carry. 

Now, 3rd step is 2 + x + x + x = 5 => x = 1

Hence, the three dgits are 1, 8, 5.

185 + 185 + 185 = 555. 

Here given that 9 = 63, 8 = 48, 7=35, ... 

The given question follows a pattern that

9 x (9 - 2) = 9 x 7 = 63

8 x (8 - 2) = 8 x 6 = 48

7 x (7 - 2) = 7 x 5 = 35

Similarly, 4 x (4 - 2) = 4 x 2 = 8.

Number of squares in the given figure is

16 + 9 + 19 + 1 = 45.