Discussion

Explanation:

To maximise the number of students who could have joined the school in 2021, we need to maximise the number of students that exit the school in 2021.

∴ We need to minimise the number of students failing in class 6.

There are 48 students in class 6 in 2021. Out of these 48, maximum 44 could have passed in class 5 and moved to class 6. Hence, minimum 4 students need to fail in class 6.

Now, since all 44 students passed from class 5 to class 6, no student failed in class 5 in 2020.

Now in 2021 all 49 students in class 5 could have come from passing class 4.
Hence, out of 59 students in class 4 in 2020, at most 49 passed to next class and hence at least 10 failed and stayed in class 4.

Similarly, we can draw the following chart.

​​​​​​​

Hence, maximum number of students who could have joined the school in 2021 is 77.

Hence, 77.

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