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Question

Points A and B are 90 km apart from each other on a highway. A car starts from A and another from B at the same time. If they go in the same direction they meet in 9 hours and if they go in opposite directions they meet in 97 hours. Speed of car starting from point A is:


A

30 km/hr

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B

90 km/hr

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C

40 km/hr

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D

220 km/hr

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Solution

The correct option is C

40 km/hr


Let X and Y be two cars starting from points A and B respectively. Let the speed of car X be x km/hr and that of car Y be y km/hr.
Case I: When the two cars move in the same direction:
Suppose two cars meet at point Q.
Distance travelled by car X = AQ
Distance travelled by car Y = BQ
Distance travelled by car X in 9 hours = 9x km AQ = 9x
Distance travelled by car Y in 9 hours = 9y km BQ = 9y

Clearly, AQ - BQ = AB [ AB = 90 km]
9x - 9y = 90 x - y = 10 . . . . (1)

Case II: When two cars move in opposite direction:
Suppose two cars meet at point P.
Distance travelled by car X = AP.
Distance travelled by car Y = BP.
In this case, two cars meet in 97 hours.

Distance travelled by car X in 97hours=97x km AP=97x

Distance travelled by car Y in 97hours=97y km BP=97y
Clearly, AP + BP = AB

97x+97y=9097(x+y)=90

x + y = 70 . . . . (2)
Adding equations (1) and (2),
x - y = 10 ....(1)
x + y = 70 .....(2)
________
2x = 80
x = 40
Substitute x = 40 in eq. (1)
40 - y = 10
y = 40 - 10 = 30
x = 40 and y = 30
Hence, speed of car starting from point A is 40 km/hr.


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