    Question

# Points A and B are 90 km apart on a highway. A car starts from A and another from B at the same time. If they travel in the same direction they meet in 9 hours and if they travel 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=90⇒97(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.  Suggest Corrections  1      Similar questions
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