Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read the question and both the 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 H 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 alone or in statement II alone are sufficient to answer the question.
Give answer d: if the data even in both the statements I and H together are not sufficient to answer the question.
Give answer e: if the data in both the statements I and II together are necessary to answer the question.
What is the speed of the boat in still water ?
I. It takes 2 hours to cover distance between A and B downstreams.
II. It takes 4 hours to cover distance between A and B upstreams.
Clearly, we have to use both equations.
Let distance between A and B = $$d$$ km
Let speed of boat in still water = $$x$$ kmph
and speed of current = $$y$$ kmph
Using, $$time = \frac{distance}{speed}$$
=> $$\frac{d}{x + y} = 2$$ ---------Eqn(1)
and $$\frac{d}{x - y} = 4$$ ---------Eqn(2)
Dividing equation (2) by (1)
=> $$\frac{x + y}{x - y} = \frac{4}{2}$$
=> $$x + y = 2x - 2y$$
=> $$2x - x = y + 2y$$
=> $$x = 3y$$
=> $$\frac{x}{y} = \frac{3}{1}$$
$$\therefore$$ Ratio between speed of boat and current is known and not the exact value.
Thus, even both statements together are insufficient.
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