# Q. Joseph visits the club on every 5th day, Harsh visits on every 24th day, while Sumit visits on every 9th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again ?

(a) Monday

(b) Wednesday

(c) Thursday

(d) Sunday

Correct Answer: (b) Wednesday

#### Question from UPSC Prelims 2021 CSAT Paper

**Explanation : **

## Club Meetings : Joseph, Harsh, and Sumit

Joseph, Harsh, and Sumit follow different visit schedules to the club. Joseph visits every **5th** day, Harsh every **24th** day, and Sumit every **9th** day.

To find the next time they will meet simultaneously, we calculate the **Least Common Multiple (LCM)** of their visit intervals (5, 24, and 9). The LCM is **360** days.

This implies that after 360 days, they will meet again. If we determine the odd days in 360, which is the remainder when dividing by 7, we get **3**.

Thus, their next meeting will be on **Sunday + 3 = Wednesday**.