Speed of a boat in still water = distance / time = 12/1 = 12 km/h
Speed against the current = 12/3 km/h
Let the speed of the current = x km/h
According to the question,
12 - x = 4

Correct Option: A

Speed of a boat in still water = distance / time = 12/1 = 12 km/h
Speed against the current = 12/3 km/h
Let the speed of the current = x km/h
According to the question,
12 - x = 4
⇒ x = 8 km/h

Let the speed in still water be x km/hr
Then, 6/x + 4 + 6/x - 4 = 2

Correct Option: C

Let the speed in still water be x km/hr
Then, 6/x + 4 + 6/x - 4 = 2
⇒ 6[ x - 4 + x + 4] = 2(x² - 16)
⇒ x² - 6x - 16 = 0
⇒ (x - 8) (x + 2) = 0
∴ x = 8 km/hr

Let speed of water current be x km/h
∴ Speed downstream = (10 + x) km/h.
Speed upstream = (10 - x) km/h
According to the question,
24/(10 + x) + 24/(10 - x) = 5

Correct Option: A

Let speed of water current be x km/h
∴ Speed downstream = (10 + x) km/h.
Speed upstream = (10 - x) km/h
According to the question,
24/(10 + x) + 24/(10 - x) = 5
⇒ 24[10 - x + 10 + x] = 5(10² - x²)
⇒ 100 - x² = (24 x 20) / 5
⇒ 100 - x² = 96
⇒ x² = 4
⇒ x = √4 = 2km/h

Speed of boat downstream = Distance covered / Time taken
= 30/2 = 15 km/h

Now, speed of boat upstream = Distance covered / Time taken
= 30/6 = 5 km/h

Correct Option: D

Speed of boat downstream = Distance covered / Time taken
= 30/2 = 15 km/h

Now, speed of boat upstream = Distance covered / Time taken
= 30/6 = 5 km/h

Now, speed of boat = (Speed download + Speed upstream) / 2
= (15 + 5) / 2 = 10 km/h

Let speed of boat be x km/h.
Given speed of current = 5 km/h
∴ Upstream speed of boat = (x -5) km/h
Downstream speed of boat = (x + 5) km/h

According to the question.
10/(x - 5) + 10/(x + 5) = 50/60

Correct Option: C

Let speed of boat be x km/h.
Given speed of current = 5 km/h
∴ Upstream speed of boat = (x -5) km/h
Downstream speed of boat = (x + 5) km/h

According to the question.
10/(x - 5) + 10/(x + 5) = 50/60
⇒ 10(x + 5 + x - 5)/( x² - 25) = 5/6
⇒ x² -24x - 25 = 0
⇒ x² - 25x + x - 25 = 0
⇒ (x - 25) (x + 1) = 0
∴ x = 25 [∴ x ≠ -1]