Question

The local bus service has $2$ lines of buses that start together at $8\text{a.m.}$ Buses on line A leave after every $20$ minutes while Buses on line B leave after every $15$ minutes. In a day, how many times do buses on both line A and B leave together between $7\text{a.m.}$ and $10\text{p.m.}$?​

• A. $13$
• B. $14$
• C. $15$
• D. $16$

Answer 1

The correct option is C $15$

Buses leave lines A and B after $20$ minutes and $15$ minutes, respectively.
LCM of $20,15⟹$
$20=2\times 2\times 5$
$15=3\times 5$
LCM $(20,15)=2\times 2\times 3\times 5=60$
So, the buses leave together after every $60$ minutes or $1$ hour.
Starting from 8 a.m., Number of times the buses leave together from 8 a.m. to 10 p.m. = 15