Let the speed of the boat in still water = x km/hr

Speed of stream = y km/hr

Now, Speed of rowing during upstream = (x-y) Km/hr

Speed of rowing during downstream = (x+y) km/hr

Given that a person rows a distance of  km upstream in  hours

Speed of rowing during upstream =

⇒ ………………..(1)

Also, the same person rows a distance of 13 km downstream in 2 hours

Speed of rowing during downstream =

⇒ …………………(2)

Adding (1) and (2)

⇒

⇒  km/hr

Hence the speed of rowing in still water = 4.5 km/hr

Now, he has to cover a distance of 45 km.

Hence , Time required =  hr

Let the number of rows = x

Let the number of students in a row = y

Hence the total number of boys = xy

If one boy is extra in a row, there would be 2 rows less

⇒

⇒

⇒ ……………(1)

If one boy is less in a row there would be 3 rows more

⇒

⇒

⇒ ……………….(2)

Adding (1) and (2)

y = 5

Put value of y in equation (1)

⇒

⇒ x = 12

Hence total number of boys =xy =  60

The system of equations will have a unique solution if and only if,

 can be any real number except -3 and 3

⇒  or

We will first solve ……………..(1) and …………….(2)

From (2)

a-b = 0

a = b………………..(3)

put in (1)

 and ……………(4)

Now solve ……………..(5)

⇒

From (3)

So a= b = ……………..(6)

From (4) and (5)

 Let the number of 25 paise coins be x and that of 10 paise coins be y, then :

⇒ …………..(1)

And

⇒ ……………….(2)

Put value of y from (2) in (1)

⇒

⇒

From (2)

y = 3x = 3(15) = 45

Hence total coins = 45 + 15 = 60

Area of triangle formed by

Area of triangle formed by

A/Q,

k²-66k+9=0