Question 20

Explanation

Delivery Schedule Analysis

We need to find the time interval for all three suppliers to deliver goods simultaneously. The concept used is the Least Common Multiple (LCM).

Given delivery schedules:

• Oil A: every $3$ days.
• Oil B: every $4$ days.
• Oil C: every $x$ days.

The first meeting occurred on April $1$, $2023$. The $11$th meeting occurs $120$ days later.

Calculating Meeting Interval

Since the first meeting has already occurred, the $11$th meeting means there is a difference of $11 - 1 = 10$ meeting intervals. The total elapsed time is $120$ days.

This means all three suppliers deliver goods simultaneously every $12$ days. This is the LCM value of their delivery schedules.

Determining the Value of x

We know that $\text{LCM}(3, 4) = 12$. For $\text{LCM}(12, x) = 12$, $x$ must be a factor of $12$ (a number that divides $12$ without a remainder).

Checking the available options:

• $5, 7, 8, 9$ are not factors of $12$.
• $6$ is a factor of $12$.

Thus, the value of $x$ that satisfies the condition is $6$.