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Quantitative Aptitude -Time,Speed and Distance- How far from station A do they meet!!!

PSA_LEVEL-UP_QNR44. Ravi and Kiran are located at two stations A and B respectively and are 600 km apart. Ravi starts on a bus from station A towards B. After two hours Kiran boards a bus from station B. How far from station A do their buses cross if the buses are speeding at constant speeds of 25 km/h and 35 km/h?

a) 260 km
b) 270 km
c) 229.16 km
d) 279.16 km

Ans:

Initial distance between station A and B = 600 km.
Ravi first starts on a bus from A and travels for 2 hours (assume he reaches a point P).
Thus, Ravi travels 25*2 or 50 km.

|A|————-|P|——————————————————|B|
<…….50…..><…………………….550……………………>

Now, effective distance between Ravi and Kiran = 600-50 = 550 km = PB
From this point P to wherever they meet (in between P and B), they take equal times with speeds 25km/h and 35 km/h respectively.

Time being equal, speed ratio is equal to the distance ratio.

Distance PB will be covered by both in the ratio 25:35 or 5:7.

If we assume, Ravi travels 5x, then Kiran travels 7x in the same time.

|A|————-|P|——————————————————|B|
<…….50…..><……………………(5x+7x)………………..>

5x+7x= 550
=> 12x = 550

5x= [550/12] * 5 = 2750/12 = 229.16

Thus, distance covered by Ravi till they meet = 50 km + 229.16 km = 279.16 km. Option d.

Alternatively, you can find out the time taken to meet (after 2 hours) as
t= Distance/Relative speed

Effective distance between Ravi and Kiran = 600-50 = 550 km = PB
Relative speed = 25 km/h + 35 km/h = 60 km/h (Since both are travelling towards each other).

Both meet after, t= 550/60 hours.
In this time, t, Ravi has travelled = 25 * 550/60 km (speed * time = distance).

Total distance travelled by Ravi = 50 km + 25 * 550/60 km

=50 (11*25/60 +1)
=50(275/60 +1)
=50 (335/60)
=1675/6
=279.16 km. Option d.

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