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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, 30
Let 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=1xx=20 kmph
b=1by=30 kmph
Speed of the bike =20 kmph
Speed of the car =30 kmph

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