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Q.
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 ?
A.
99
B.
100
C.
89
D.
1
View Answer
Correct choice: A
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 SPSR = SPSQxSQSR = (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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