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08 Jul 2026, 22:11
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Bunuel
Bus 2 leaves 6 Hrs after Bus 1 so distance travelled by Bus 1 in 6 Hrs = 6*50=300 Km
using relative speed concept - time taken by Bus 2 to meet Bus 1 = distance between Bus1 and Bus 2 / their relative speed.
time = 300/(80-50) => time = 10 Hrs
Lets say if Bus 1 leaves at midnight 12:00 then Bus 2 leaves at 06:00 AM and Bus 2 meets Bus1 at 04:00 PM (as time taken by Bus 2 to meet Bus 1 is 10 Hrs).
Now we need to find difference in departure time of Bus 3 and Bus 1 such that Bus 2 and Bus 3 meets Bus 1 at the same time.
As Bus3's speed is 100 km/hr so it must depart after Bus 2 to meet Bus 2 => Bus 3 should depart after 06 Hrs this leaves out us with options C, D and E.
Now we can check for options.
for (C)
If Bus leaves at 08:00 i.e. if time difference is 08 hrs then distance between Bus1 and Bus3 = distance travelled by Bus1 in 8 hrs = 400 km.
time to meet = 400 / (100-50) = 8 hrs.
so Bus 3 departs at 08:00 and meet Bus 1 after 8 Hrs at 04:00 PM which is same as Bus2 so C should be the answer.
rungtamehul
Joined: 03 Aug 2025
Last visit: 15 Aug 2026
Posts: 26
Given Kudos: 195
Location: India
Concentration: General Management, Strategy
Schools: ISB HEC Sept '27 INSEAD Aug '27
GMAT Focus 1: 705 Q88 V85 DI82 
GPA: 7.8
08 Jul 2026, 22:48
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According to the question, at the point of catch-up, all the three buses would have travelled for the same distance, at different speeds and for different time
To calculate how many hours later does the Bus 3 leave after Bus 1, we need to calculate the distance of the catch-up point from Riverton. We can calculate it using Bus 1 and Bus 2
Bus 1 travels for time period t at 50km/hr
Bus 2 travels for time period t-6 at 80km/hr
Since the distance travelled for B1 and B2 are the same, we get 50t = 80(t-6)
Solving the above equation, we get t = 16 hours
Therefore, the distance travelled by all three buses till the catchup point is 800 km
From this we can get that Bus 3 travelled for 8 hrs, therefore it left Riverton 8 hrs after Bus 1
To calculate how many hours later does the Bus 3 leave after Bus 1, we need to calculate the distance of the catch-up point from Riverton. We can calculate it using Bus 1 and Bus 2
Bus 1 travels for time period t at 50km/hr
Bus 2 travels for time period t-6 at 80km/hr
Since the distance travelled for B1 and B2 are the same, we get 50t = 80(t-6)
Solving the above equation, we get t = 16 hours
Therefore, the distance travelled by all three buses till the catchup point is 800 km
From this we can get that Bus 3 travelled for 8 hrs, therefore it left Riverton 8 hrs after Bus 1
Bunuel
08 Jul 2026, 22:57
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step 1. find km travle by 1st bus before 2nd bus even left that woll be 50*6=300 (how we get 6hr because that the time 2nd bus left )
step 2. now we have to focus on difference in speed between two bus that is 30km/hr (80-50) and then see by calcualtion that what is the number at which both bus has same number of km travel and that number will be 800 km (how first you try numbers that are whole ie 400km 800km why its easy to calculate , so if you try 400km your bus 1 will 150 km ahead of bus 2 then try 800 for that the exact match then you knw that bus 2 travel 800km in 10 hr and bus 1 travel in 16 hr )
step 3. now you just have to divide 800/100(distance/speed=time) hence time for bus 3 to catch b1 and b2 at same time. but thats not the final answer for that we have to subtract b1 time - b3 time which is 16-8=8.
answer = C
step 2. now we have to focus on difference in speed between two bus that is 30km/hr (80-50) and then see by calcualtion that what is the number at which both bus has same number of km travel and that number will be 800 km (how first you try numbers that are whole ie 400km 800km why its easy to calculate , so if you try 400km your bus 1 will 150 km ahead of bus 2 then try 800 for that the exact match then you knw that bus 2 travel 800km in 10 hr and bus 1 travel in 16 hr )
step 3. now you just have to divide 800/100(distance/speed=time) hence time for bus 3 to catch b1 and b2 at same time. but thats not the final answer for that we have to subtract b1 time - b3 time which is 16-8=8.
answer = C
