Question

Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and

A boat takes a total time of three hours to travel downstream from P and Q and upstream back from Q to P. What is the speed of the boat in still water?
I. The speed of the river current is 1 km per hour.
II. The distance between P and Q is 4 km.

A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer

Answer 1

To determine the speed of the boat in still water, both the speed of the river current and the distance between points P and Q are necessary. Statement I provides the speed of the current, and Statement II provides the distance. The correct option is E, which states that both statements are necessary to answer the question.

Step-by-step explanation:

To determine if the data provided in statements I and II is sufficient to answer the question 'What is the speed of the boat in still water?' when a boat travels downstream from P to Q and upstream back from Q to P in a total time of three hours, we need to examine both statements for their relevance and sufficiency.

Statement I: The speed of the river current is 1 km per hour. This alone does not provide enough information to answer the question since we do not know the distance between P and Q or the speed of the boat in still water.

Statement II: The distance between P and Q is 4 km. Knowing the distance helps, but without the speed of the river current or the speed of the boat in still water, we cannot determine the time it would take to travel upstream and downstream.

Only when we combine Statement I (the speed of the river current is 1 km per hour) with Statement II (the distance between P and Q is 4 km), we can calculate the speed of the boat in still water. With both pieces of information, we can find the speed of the boat in still water by using the formula for speed in downstream and upstream travel. Therefore, both Statement I and Statement II are necessary to answer the question.

The correct option in the final part is E. Both I and II are necessary to answer.