Boats and Streams – Data Sufficiency 1

Boats and Streams – Data Sufficiency 1

Directions to Solve

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

  • Give answer (A) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
  • Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
  • Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.
  • Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
  • Give answer(E) if the data in both Statements I and II together are necessary to answer the question.
1.
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: Option E

Explanation:

 I. Speed of the current = 1 km/hr.

II. PQ = 4 km.

Let the speed of the boat in still water be x km/hr. Then,

4 + 4 = 3. This gives x.
(x + 1) (x – 1)

 Correct answer is (E).

2.
What is the speed of the boat in still water?
I. It takes 2 hours to cover the distance between A and B downstream.
 II. It takes 4 hours to cover the distance between A and B upstream.
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: Option D

Explanation:

Let AB = x km.

 I. Speed downstream = x km/hr
2
II. Speed upstream = x km/hr.
4
Speed of boat in still water = 1 x + x km/hr.
2 2 4

Thus, I and II both even do not give the answer.

 Correct answer is (D).

3.
What is the speed of the boat in still water?
I. The boat covers a distance of 48 kms in 6 hours while running upstream.
 II. The boat covers the same distance in 4 hours while running downstream.
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: Option E

Explanation:

 I. Speed upstream = 48 km/hr = 8 km/hr.
6
II. Speed downstream = 48 km/hr = 12 km/hr.
4
Speed of the boat = 1 (8 + 12) km/hr = 10 km/hr.
2

Thus, I and II together give the answer.

 Correct answer is (E).

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