NIMCET 2024 — Reasoning PYQ

1. Find the LCM of the visit intervals:

Ramu's cycle is $15$ days and Samu's cycle is $20$ days.

• Prime factorization of $15=3\times 5$

• Prime factorization of $20=2^2\times 5$

• $\text{LCM}(15,20)=2^2\times 3\times 5=60$

This means they meet every $60$ days.

2. Account for the time passed:

The problem states they met $5$ days ago.

Let $T$ be the total interval between meetings and $P$ be the days already passed since the last meeting.

• Total interval ($T$) = $60$ days

• Days passed ($P$) = $5$ days

3. Calculate the remaining days from today:

The number of days until the next meeting from today is:

Conclusion:

Ramu and Samu will meet again in 55 days from today.