Correct Answer - Option 2 : 6 kmph
Given:
10 km upstream + 12 km downstream = 4 hours
14 upstream + 20 downstream = 6 hours
Concept Used:
Speed = Distance/Time
Speed in upstream = x – y
Speed in downstream = x + y
Where,
x is a speed of a boat in still water,
y is a speed of a stream
Calculations:
According to the question,
10/(x – y) + 12/(x + y) = 4
14/(x – y) + 20/(x + y) = 6
Let (x – y) be a and (x + y) be b,
⇒ 10/a + 12/b = 4 ----(I)
⇒ 14/a + 20/b = 6 ----(II)
Solving equation (I),
⇒ 10b + 12a = 4ab
Multiplying above equation by 3,
⇒ 30b + 36a = 12ab ----(III)
Solving equation (II),
⇒ 14b + 20a = 6ab
Multiplying above equation by 2,
⇒ 28b + 40a = 12ab ----(IV)
Comparing equation (III) and (IV), we get
⇒ 30b + 36a = 28b + 40a
⇒ 2b = 4a
⇒ b = 2a
Putting the values of a and b,
⇒ x + y = 2(x – y)
⇒ x + y = 2x – 2y
⇒ y = x/3
Putting the value in given condition,
⇒ 10/(x – y) + 12/(x + y) = 4
⇒ 10(x – x/3) + 12(x + x/3) = 4
⇒ 10/(2x/3) + 12(4x/3) = 4
⇒ 15/x + 9/x = 4
⇒ 24/x = 4
⇒ x = 24/4 = 6
∴ The speed of a boat in still water is 6km/hr.
