Question

Ramu visits Delhi every 15 days and Samu goes to Delhi every 20 days. They met at Delhi 5 days back. After how many days, from today, they will meet at Delhi next time?

• A. 35
• B. 60
• C. 55
• D. 65

Hint:

When solving problems involving repeated events, find the least common multiple (LCM) to determine when the events will coincide again.

Answer 1

The Correct Option is C

Step 1: Find the least common multiple (LCM) of the visit intervals. Ramu visits Delhi every 15 days.
Samu visits Delhi every 20 days.
The first step is to find the LCM of 15 and 20, as this will tell us after how many days both will visit Delhi at the same time. The prime factorizations are: \[ 15 = 3 \times 5, \quad 20 = 2^2 \times 5. \] The LCM is: \[ LCM(15, 20) = 2^2 \times 3 \times 5 = 60. \] Step 2: Adjust for the fact they met 5 days ago. Since they met 5 days ago, we subtract 5 from the LCM to get the next meeting time: \[ 60 - 5 = 55. \] Thus, the next time they will meet at Delhi is after: \[ \boxed{55 { days}}. \]