P is 300 km eastward of O and Q is 400 km north of O. R is exactly in the middle of Q and P. The distance between Q and R is

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Q: 136 (IAS/1997)
P is 300 km eastward of O and Q is 400 km north of O. R is exactly in the middle of Q and P. The distance between Q and R is

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,4,3,4,1,0,2

keywords: 

{'distance': [0, 3, 3, 3], 'km': [0, 0, 2, 1]}

The distance between Q and R is being asked in the question. Q and R are positioned such that R is in the middle of Q and P. Since, the straight line distance between Q and P represents a diagonal of a right-angled triangle with sides of 300 km (eastward journey from O to P) and 400 km (northward journey from O to Q); R, lying in the middle splits this diagonal into two equal halves. The exact length of half of this diagonal is not given in the question, but it can be calculated using Pythagoras theorem. However, such calculation is not required here as option 1, saying `250 km`, is the only one suggesting a division of the diagonal into equal parts. Other options suggest different measurements. Option 2 suggests a distance that is equal to O to P; option 3 suggests a larger arbitrary distance; and option 4 suggests the multiplication of 250 km by √2, which also does not represent any division of the diagonal or relevant measurement. Thus, answer 1 is correct.

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