Instructions

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.

Question 110

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.

Solution

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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