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Question

# A person travels a distance of 100 km by bike and 120 km by car in a span of 10 hrs. He then travels 200 km by bike and 180 km by car in a span of 16 hrs. The speed of bike and car, respectively, in kmph is: [1 mark]

A
30, 20
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B
20, 30
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C
30, 40
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D
40, 30
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Solution

## The correct option is B 20, 30Let the speed of the bike =x speed of car =y Time=DistanceSpeed In the first case, the time taken to travel by bike =100xhr The time taken to travel by car =120yhr Total time = Time taken to travel by bike + car 10=100x+120y...(1) Similarly, in the second case, 16=200x+180y....(2) Now, by assuming 1x=a and 1y=b, wee get, 10=100a+150b....(3) 16=200a+18b....(4) Multiplying (3) with 2, we get, 20=200a+300b....(5) (5)−(4), we get, 4=120b ⇒b=130 Substituting b in (3), we get, 10=100a+15030 ⇒a=120 ∵a=1x⇒x=20 kmph ∵b=1b⇒y=30 kmph ∴ Speed of the bike =20 kmph Speed of the car =30 kmph

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