Question

2) (a) From a certain city, busses start for four different places every 15,20,25 and 30 minutes starting
from 8.00 a.m. At what time, for the first time after 8.00 a.m., would all the busses start together
again?​

Answer 1

The buses will start again at 1:00 pm; that is, after 5 hours.

Explanation: the LCM of 15,20,25, and 30 minutes is 300 minutes; that is, 5 hours

Answer 2

The buses will start together again after 5 hours i.e. 1 p.m.

Given:

From a certain city, buses start for four different places every 15,20,25 and 30 minutes starting from 8.00 a.m.

To Find:

At what time, for the first time after 8.00 a.m., would all the buses start together again.

Solution:

We can simply solve this problem by using the following mathematical process.

We have to find the lowest common multiple of 15,20,25 and 30

This can be done through prime factorisation.

15 = 5 × 3

20 = 2 × 2 × 5

25 = 5 × 5

30 = 2 × 3 × 5

∴ LCM = 5 × 3 × 5 × 2 × 2

300

So, the buses will start again after 300 minutes

300 minutes = $\frac{300}{60}$ hours

i.e. 5 hours

The buses will start together after 5 hours i.e. 1 p.m.

Hence, the buses will start together at 1 p.m.

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