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Mathematics

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

Assertion (A) : The speed of the boat in still water = (20−182)\Big(\dfrac{20 - 18}{2}\Big) km/hr.

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

  1. A is true, R is false.

  2. A is false, R is true.

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

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

Quadratic Equations

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Answer

A is false, R is true.

Reason

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=20x−y=16+++2x=20+16⇒x=20+162\begin{matrix} & x & + & y & = & 20 \ & x & - & y & = & 16 \ & + & + & & & + \ \hline & 2x & & & = & 20 + 16 \ \Rightarrow & x & & & = & \dfrac{20 + 16}{2} \ \end{matrix}

⇒ x = 362\dfrac{36}{2} = 18 km/hr

Subtracting equation (2) from (1), we get

x+y=20x−y=16−−−2y=20−16⇒y=20−162\begin{matrix} & x & + & y & = & 20 \ & x & - & y & = & 16 \ & - & - & & & - \ \hline & & & 2y & = & 20 - 16 \ \Rightarrow & & & y & = & \dfrac{20 - 16}{2} \ \end{matrix}

⇒ y = 42\dfrac{4}{2} = 2 km/hr

According to Assertion, the speed of the boat in still water = (20−182)\Big(\dfrac{20 - 18}{2}\Big) km/hr = 22\dfrac{2}{2} km/hr = 1 km/hr.

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

Hence, option 2 is the correct option.

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