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Two cars P and Q start at the same time from A and B which are 120 km apart. If the two cars travels in opposite directions, they meet after one hour and if they travel in same direction from A towards B, then P meets Q after 6 hours. The speed of car P is
Answer: (c)
Let speed of car P be x km/hr and car Q be 4 km/hr. When cars are moving in opposite directions
$120/{x+y}=1$ ⇒ x+y=120 ...(1)
When cars are moving in same direction
$120/{x-y}=6$ ⇒6x-6y = 120 ...(2)
⇒x-y=20
From (1) and (2)
x = 70 km/hr, y = 50 km/hr
∴ speed of car P = 70 km/hr.
A boat goes 40 km upstream in 8 hours and 36 km downstream in 6 hours. The speed of the boat in still water is ________ km/hr.
Answer: (a)
Boat's upstream speed = ${40}/8$ = 5 km/hr
Boat's downstream speed = ${36}/6$ = 6 km/hr
∴ Speed of boat in still water = ${5+6}/2$ = 5.5 km/hr
A car travels a distance of 45 kms at the speed of 15 kmph. It covers the next 50 kms of its journey at the speed of 25 kmph and the last 25 kms of its journey at the speed of 10 kmph. What is the average speed of the car?
Answer: (e)
Time taken to cover a distance of 45 kms
$\text"Distance"/\text"Speed"$ = $45/15$ = 3 hours
Time taken to cover a distance of 50 kms
= $50/25$ = 2 hours
Time taken to cover distance of 25 kms
= $25/10$ = 2.5 hours
Total distance = (45 + 50 + 25) kms = 120 kms
Total time = (3 + 2 + 2.5) hours = 7.5 hours
∴Required average speed = $120/7.5$ = 16 kmph
A train 75 metres long overtook a person who was walking at the rate of 6 km an hour, and passed him in 7$1/2$ seconds. Subsequently it overtook a second person, and passed him in 6$3/4$ seconds. At what rate was the second person travelling?
Answer: (c)
Relative speed of the train and first person
${75}/{{15}/2} = 10 m/s = {18}/5$ m/s = 36 m/s
∴ speed of the train = 36 + 6 = 42 km/hr
Now, relative speed of the train and 2nd person
= ${75}/{27} × 4m/s = {300}/{27} × {18}/5$ = 40km/hr
Shortcut: Speed of 2nd person = Relative speed of train with respect to 1st person + Speed of first person – Relative speed of train with respect to 2nd person
= $({75}/{{15}/2} × {18}/5) + 6 - ({75}/{27} × 4 × {18}/5)$ = 36 + 6 - 40 = 2 km/hr
A train leaves station X at 5 a.m. and reaches station Y at 9 a.m. Another train leaves station Y at 7 a.m. and reaches station X at 10: 30 a.m. At what time do the two trains cross each other ?
Answer: (a)
Let the distance between X and Y be x km.
Then, the speed of A is
$x/4$ km/h and that of B is $2x/7$ km/h.
Relative speeds of the trains
= $(x/4+{2x}/7)={15x}/28$ km / h
Therefore the distance between the trains at 7 a.m.
= $x-x/2=x/2$ km
Hence, time taken to cross each other
$ {x/2}/{{15x}/28}=x/2×28/{15x}=14/15×60=56min$
Thus, both of them meet at 7 : 56 a.m.
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