Two cars start from 2 cities P and Q at same time. Car A which started from city P travels 25% of the distance at 75 Km/hr and next 50% distance at 45 Km/hr and remaining distance at 50 Km/h. At the same time Car B which started from city Q covered its journey in 3 equal phases of time at a speed of 30 Km/h, 60 Km/h and 90 Km/h. If the distance P and Q is 900Km, find the time after which the two cars cross each other?

Question

Two cars start from 2 cities P and Q at same time. Car A which started from city P travels 25% of the distance at 75 Km/hr and next 50% distance at 45 Km/hr and remaining distance at 50 Km/h. At the same time Car B which started from city Q covered its journey in 3 equal phases of time at a speed of 30 Km/h, 60 Km/h and 90 Km/h. If the distance P and Q is 900Km, find the time after which the two cars cross each other?

12.60 hours
9.04 hours
5.00 hours
10.02 hours
None of these

LohaHridoy

10 views

2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 2 : 9.04 hours

For car A:

Distance between 2 cities = 900 Km

25% of the distance = 900 × 1/4 = 225 Km

Speed = 75 Km/hr

∴ Time = 225/75 = 3 hrs

50% of the distance = 900 × 1/2 = 450 Km

Speed = 45 Km/hr

Time = 450/45 = 10 hours

Remaining distance = 900 – (225 + 450) = 225 Km

Speed = 50 Km/hr

Time = 225/50 = 4.5 hours

Total time taken = 3 + 10 + 4.5 = 17.5 hrs

For car B:

Since B covered its journey in 3 equal phases of time.

Average Speed = (30 + 60 + 90)/3 = 60 Km/h

⇒ B travels at an average speed of 60 Km/h.

Distance between 2 cities = 900 Km

Total time = 900/60 = 15 hrs

∴ B travels in 1^st 5 hours = 30 × 5 = 150 Km

B travels in 2^nd 5 hours = 60 × 5 = 300 Km

B travels in 3^rd 5 hours = 90 × 5 = 450 Km

After 5 hours A will be at a distance = (225 + 90) Km = 325 Km

After 5 hours B will be at a distance = 150 Km

Distance between them = 900 – (325 + 150) = 425 Km

Now, Speed of Car A = 45 Km/hr

Speed of B = 60 Km/hr

They travel in opposite direction.

∴ Relative Speed = 45 + 60 = 105 Km/h

Time = 425/105 = 4.04 hrs

Total time = (5 + 4.04) hrs = 9.04 hrs