A goat is tied to two poles P and Q with ropes that are 15-metre long. P and Q are 20-metre apart as shown in the given diagram: Which one of the following shaded portions indicates the total area over which the goat can graze ?

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Q: 147 (IAS/2000)
A goat is tied to two poles P and Q with ropes that are 15-metre long. P and Q are 20-metre apart as shown in the given diagram:
Which one of the following shaded portions indicates the total area over which the goat can graze ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,2,3,0,2,1,2

keywords: 

{'diagram': [0, 3, 2, 5], 'ropes': [0, 1, 0, 0], 'goat': [5, 2, 1, 5], 'shaded portions': [0, 1, 0, 0], 'total area': [1, 1, 0, 0], 'metre': [0, 3, 4, 3]}

The goat is tied to two poles with ropes that are 15-metre long, has access to an area denoted by a circle with the pole as the center and the length of the rope as the radius. Therefore, the grazing area around each pole is a circular region with a 15-metre radius.

Option 1: This only includes the area within the reach of one pole, thus excluding the second pole. Therefore, it`s not the complete grazing area.

Option 2: The goat can reach the full 15-metre radius from both poles P and Q, this overflowing in some areas where the circles overlap, and creating a sort of figure-eight (8) shape. This covers the most ground for the goat, so this is the correct answer.

Option 3: Though this area overlaps the two poles, the total combined overlap does not make up a complete circle from either pole, thus providing less grazing area than needed.

Option 4: While covering the entire 15-metre radius from either pole, it excludes the overlapping area. Thus, it is smaller than the total reachable area.