Question

The speed of a boat downstream is 20 km/h and upstream is 16 km/h.

Assertion (A): The speed of boat in still water = `(20-18)/2` km/h.

Reason (R): If speed of boat in still water is x km/h and speed of stream is y km/h, the speed downstream = (x + y) km/h and speed upstream = (x - y) km/h

विकल्प

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

A is false, R is true.

Explanation:

Given,

Speed of boat downstream = 20 km/hr

Speed of boat upstream = 16 km/hr

Let the speed of boat in still water is x km/hr and the speed of stream is y km/hr.

Speed of boat downstream = x + y

⇒ x + y = 20      ...... (1)

Speed of boat upstream = x − y

⇒ x − y = 16      ...... (2)

Adding equation (1) and (2), we get

   x + y = 20

   x − y = 16

 +    +      +               
        2y = 20 − 16

⇒ 2y = `(20 − 16)/2`

⇒ y = `4/2`​ = 2 km/hr

According to Assertion, the speed of the boat in still water = `(20-18)/2` km/h = `2/2` km/hr = 1 km/hr.

So, Assertion (A) is false but Reason (R) is true.