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P, Q and R start simultaneously from A to B. P reaches B, turns back and meet Q at a distance of 11 km from B. Q reached B, turns back and meet R at a distance of 9 km from B. If the ratio of the speeds of P and R is 3:2, what is the distance between A and B ?

Correct Answer: 99

Explanation:

Let, Distance between A and B = d


 


Distance travelled by P while it meets Q = d + 11


 


Distance travelled by Q while it meets P = d – 11


 


Distance travelled by Q while it meets R = d + 9


 


Distance travelled by R while it meets Q = d – 9


 


Here the ratio of speeds of P & Q => SP : SQ = d + 11 : d – 11


 


The ratio of speeds of Q & R => SQ : SR = d + 9 : d – 9


 


But given Ratio of speeds of P & R => P : R = 3 : 2


  S P S R   =   S P S Q x S Q S R   =   d + 11 d + 9 d - 11 d - 9


 


=>  d + 11 d + 9 d - 11 d - 9  = 3/2


 


=>  d = 1, 99


 


=> d = 99 satisfies.


 


Therefore, Distance between A and B = 99


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