Comprehension:

In a coaching class, some students register online, and some others register offline. No student registers both online and offline; hence the total registration number is the sum of online and offline registrations. The following facts and table pertain to these registration numbers for the five months - January to May of 2023. The table shows the minimum, maximum, median registration numbers of these five months, separately for online, offline and total number of registrations. The following additional facts are known.

1. In every month, both online and offline registration numbers were multiples of 10.

2. In January, the number of offline registrations was twice that of online registrations.

3. In April, the number of online registrations was twice that of offline registrations.

4. The number of online registrations in March was the same as the number of offline registrations in February.

5. The number of online registrations was the largest in May.

	Minimum	Maximum	Median
Online	40	100	80
Offline	30	80	50
Total	110	130	120

What was the total number of registrations in April?

To find the total number of registrations in April, we can analyze the given information step-by-step.

Let the online registrations, offline registrations, and total registrations in month M be denoted by ${\text{On}}_M$, ${\text{Off}}_M$, and ${\text{Tot}}_M$ respectively, where ${\text{Tot}}_M={\text{On}}_M+{\text{Off}}_M$.

From the table, we have the following parameters for the five months (January to May 2023):
- Online registrations: Minimum = 40, Maximum = 100, Median = 80
- Offline registrations: Minimum = 30, Maximum = 80, Median = 50
- Total registrations: Minimum = 110, Maximum = 130, Median = 120

Step 1: Analyze January registrations
According to Fact 2, the number of offline registrations in January was twice that of online registrations:
${\text{Off}}_{\text{Jan}}=2\times {\text{On}}_{\text{Jan}}$

We know that the maximum offline registration in any month is 80. Therefore:
${\text{Off}}_{\text{Jan}}\le 80\Rightarrow 2\times {\text{On}}_{\text{Jan}}\le 80\Rightarrow {\text{On}}_{\text{Jan}}\le 40$

Since the minimum online registration in any month is 40, ${\text{On}}_{\text{Jan}}$ must be exactly 40. Consequently, we have:
${\text{On}}_{\text{Jan}}=40$
${\text{Off}}_{\text{Jan}}=80$

Step 2: Analyze April registrations
According to Fact 3, the number of online registrations in April was twice that of offline registrations:
${\text{On}}_{\text{Apr}}=2\times {\text{Off}}_{\text{Apr}}$

The total registrations in April is given by:
${\text{Tot}}_{\text{Apr}}={\text{On}}_{\text{Apr}}+{\text{Off}}_{\text{Apr}}=2\times {\text{Off}}_{\text{Apr}}+{\text{Off}}_{\text{Apr}}=3\times {\text{Off}}_{\text{Apr}}$

Since registrations are multiples of 10, ${\text{Off}}_{\text{Apr}}$ must be a multiple of 10. Let's test the possible values of ${\text{Off}}_{\text{Apr}}$ (where the range of offline registrations is between 30 and 80):
- If ${\text{Off}}_{\text{Apr}}=30$, then ${\text{Tot}}_{\text{Apr}}=3\times 30=90$. This is invalid because the minimum total registration is 110.
- If ${\text{Off}}_{\text{Apr}}=40$, then ${\text{Tot}}_{\text{Apr}}=3\times 40=120$. This is a valid total registration (since the total registration range is 110 to 130). In this case, ${\text{On}}_{\text{Apr}}=80$.
- If ${\text{Off}}_{\text{Apr}}=50$, then ${\text{Tot}}_{\text{Apr}}=3\times 50=150$. This is invalid because the maximum total registration is 130.

Therefore, the total number of registrations in April is 120.