Published by:
CGP EDU Academic Team
Published on: August 13, 2026
A dispatch rider is in open country at a distance of 6 km from the nearest point P of a straight road. He wishes to proceed as quickly as possible to a point Q on the road 20 km from P. If his maximum speed across country is 40 km/hr, then at what distance from P, he should strike the road at the speed 50 km/hr.
Text Solution
Verified by ExpertsThe correct answer is:
A
Let A be the initial position of rider.
Let, PB = x
∴ QB = 20 – x
and AB = 
= 
km.
∴ Total time T,
T = 
+ 
= 
. 
– 
For maximum and minimum value, must have
= 0
⇒ 
= 
or 
= 
or 
– x 2 = 36
⇒ x 2 = 
⇒ x = 
= 8 km.
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