Question

3 cars with speeds 30 km/hr, 42 km/hr and 36 km/hr are required to cover a distance of 350 km. All the cars start from same point at same time, then after how much time will all the cars meet?
1. 175/3 hours
2. 350/3 hours
3. 25 hours
4. 195/3 hours

Answer 1

Correct Answer - Option 1 : 175/3 hours

Calculations:

Distance to be covered = 350 km

Speed of first car = 30 km

⇒ Time taken by first car to cover 350 km = 350/30 = 35/3 hrs

Speed of second car = 42 km

⇒ Time taken by second car to cover 350 km = 350/42 = 25/3 hrs

Speed of third car = 36 km

⇒ Time taken by third car to cover 350 km = 350/36 = 175/18 hrs

Time when all cars will meet = LCM of (35/3, 25/3, 175/18)

⇒ Time when all cars will meet = 175/3 hrs

∴ The time after which all cars will meet is 175/3 hours.

Time, when all cars will meet, is lcm of time taken by each car.

Speed = Distance/Time

LCM of (x/y, p/q) = LCM of (x, p)/HCF of (y, q)