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State true or false.

Distance between two places A and B is 210 km. Two cars start simultaneously from A and B in opposite directions and the distance between them after 3 hours is 54 km. If the speed of one car is less than that of another by 8 km/hr, then the speed of each car will be 30 km/hr and 22 km/hr respectively.

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True

False

answer is A.

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Detailed Solution

We have to check if the speed of each car will be 30 km/hr and 22 km/hr respectively.
For calculating the speed:

speed = D i s t a n c e time

Suppose the car that starts from place A is P and the car that starts from place B is Q.
Let the speed of car P

= x

km/hr.
Thus, speed of car Q

= (x − 8)

km/hr.
And, distance traveled by car-P in

3

hours = 3x km.
Distance traveled by car-Q in

3

hours

= 3 (x − 8) = 3 x − 24

km.
Also, the distance between the cars after

3

hours is 54 km.
Distance between the two cars after

3

hours=
Total distance-(Distance traveled by Car P) + (Distance traveled by Car Q)
Putting these values we get:
54=210-3x-(3x-24)

⇒ 54 = 210 − 6 x + 24

⇒ 54 = 234 − 6 x

⇒ 6 x = 234 − 54

⇒ 6 x = 180

Now dividing by

6

x = 30

So, the speed of car P is

x = 30

km/hr.
The speed of car Q is

x − 8 = 30 − 8 = 22

km/hr
Thus, the respective speeds of the cars are 30 km/hr and 22 km/hr.
Hence, the given statement is true.
Therefore, option 1 is correct.

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