Strait is nothing but a narrow passage of water which connects two seas or other large areas of water. Here Palk strait is the strait that separates India from Sri Lanka.

The given math puzzle follows a logic that,

1 + 4 = 5 => 1 x 4 + 1 = 5

2 + 5 = 12 => 2 x 5 + 2 = 12

3 + 6 = 21 => 3 x 6 + 3 = 21

Similarly,

8 + 11 = > 8 x 11 + 8 = 96.

From the given data,

3500x7xt/100 = 500

=> t = 100/49 years

Now, in the second case

The interest per year = 49/100 x 800 = 392

 => 4900 x 1 x r/100 = 392

=> r = 8%

Oligarchy is a form of government in which the power rests with the small group of people.

From the given data,

let the amounts invested be 4p, 5p and 3p

Net profit = Total profit - Total loss

= 10x5p/100 + 25x3p/200 - 20x4p/100

= 0.875p - 0.8p

= 0.075p

Therefore, profit% = (Net profit/Total investment) x 100

= 0.075 x 100/12 

= 0.0625%

Time taken by both Meghana and Ganesh to work together is given by =

t1 x t2

Where

$$\begin{gathered} t1 = 32 hrs \\ t2 = 12 12 hrs = 252 hrs \end{gathered}$$

Therefore, time took by both to work together = 

32 x 252 = 16 x 25 = 4 x 5 = 20 hrs

The given number series is 10, 6, 8, 15, ?

10

10 x 0.5 + 1 = 6

6 x 1 + 2 = 8

8 x 1.5 + 3 = 15

15 x 2 + 4 = 34

Hence, the next number in the given series is 34.