GATE Questions

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A sponge is a porous material. Rubber is an elastic material. 

Since Rubber is not a Massive or solid and not an inflexible thing, it is elastic. 

A line is an undefined term because of it :

1. Contains an infinite number of points

2. can be used to create other geometric shapes

3. is a term that does not have a formal definition

In Geometry, unless it's stated, a line will extend in one dimension and goes on forever in both ways.

Given numbers are 585 546 514 404 206 369
Then interchanging the 1st and 3rd digits of the given numbers, we get
585 645 415 404 602 963
Now, arranging them in ascending order
963 645 602 585 415 404
Then the last second number is 415.

Doing more work in less time, results in an increase in power to do a work.

Let the actual distance be t kms

Now, According to the data,

$$\begin{gathered} 5t + 860 = 6t \\ => 560t + 860 = 6t \\ => 60t + 8 = 72t \\ => 8 = 12t \\ => t = 8/12 = 2/3 hrs \end{gathered}$$

Now, the total distance = 6t = 6 x 2/3 = 2 x 2 = 4 kms.

Let the speed of the boat in still water is 'w'

Speed of the current is 'c'

Let the distance between two places is 'd'

According to the question, motorboat takes half time to cover a certain distance downstream than upstream.

dw+c = 12dw-c

=> 2w - 2c = w + c

=> w = 3c

=> c : w = 1 : 3

Hence, the ratio between rate of current(c) and rate of boat in still water(w) = 1 : 3

In first he got Rs. 990

But in second he lost Rs. 1980

So he lost Rs. 990.