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Question

# A takes 3 hours more than B to walk 30 km. But, if A doubles his pace, he is ahead of B by 11/ 2 hours. Find their speed of walking

A
A's speed = 5km/hr, B's speed = 8 km/hr
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B
A's speed = 15/2km/hr, B's speed = 6 km/hr
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C
A's speed = 10/3km/hr, B's speed = 5 km/hr
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D
Data insufficient
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Solution

## The correct option is C A's speed = 10/3km/hr, B's speed = 5 km/hrLet the speed of A and B be x km/hr and y km/hr Time taken by A to cover 30km 30xhrsTime taken by B to cover 30km 30yhrsAccording to the question ⇒30x−30y=3⇒10x−10y=1...eq1 If A double his pace then the speed of A is 2x km/hrtherefore time taken by A to cover the 30 = 30/2xhrs And time taken by B to cover the 30KM = 30/yhrsNow according to the question⇒30y−302x=32⇒10y−5x=12⇒−10x+20y=1...eq2Now we assume 1x=u and 1y=vPutting the u and v in eq1 and eq 2 we get⇒10u−10v=1...eq3⇒−10u+20v=1...eq4Adding eq3 and eq4 we get⇒10v=2⇒v=210⇒v=15=1y→y=5Put v=15 in eq3⇒10u−3=0⇒u=310=1x⇒x=103Hence, the speed of A = 10\3 km/hr The speed of B=5 km/hr respectively

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