Question

Three subway lines arrive at a station at the same time. Line P arrives at the station every 15 minutes, line Q arrives every 25 minutes, and line R arrives every 30 minutes. How long must one wait for all three lines to arrive at the station at the same time again?

• A. 90 min
• B. 120 min
• C. 210 min
• D. 150 min

Answer 1

The correct option is D 150 min

The intervals of time are 15 minutes, 25 minutes, and 30 minutes.

The least common multiple of these numbers will give the time at which all the three lines will arrive again.

Let us find the LCM of these intervals.


So, the LCM of the numbers
$=5\times 3\times 5\times 2$

= 150 min

Hence, all of the three lines will arrive again after 150 minutes.