Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur are four musicians. Each of them started and completed their training as students under each of three Gurus — Pandit Meghnath, Ustad Samiran, and Acharya Raghunath between 2013 and 2024, including both the years. Each Guru trains any student for consecutive years only, for a span of 2, 3, or 4 years, with each Guru having a different span. During some of these years, a student may not have trained under these Gurus; however, they never trained under multiple Gurus in the same year. In none of these years, any of these Gurus trained more than two of these students at the same time. When two students train under the same Guru at the same time, they are referred to as Gurubhai, irrespective of their gender.

The following additional facts are known.

1. Ustad Samiran never trained more than one of these students in the same year.

2. Acharya Raghunath did not train any of these students during 2015-2018, as well as during 2021-24.

3. Ananya and Devendra were never Gurubhai; neither were Bhaskar and Charu. All other pairs of musicians were Gurubhai for exactly 2 years. 4. In 2013, Ananya and Bhaskar started their trainings under Pandit Meghnath and under Ustad Samiran, respectively

In which of the following years were Bhaskar and Devendra Gurubhai?

The correct answer is 2022.

First, let's determine the training spans (2, 3, or 4 years) for each of the three Gurus. The total timeframe is from 2013 to 2024, which covers exactly 12 years. We are given that Acharya Raghunath did not train anyone during 2015-2018 or 2021-2024. This leaves only two possible windows for him: 2013-2014 (2 years) and 2019-2020 (2 years). Since he must train all four students and can train a maximum of two students at the same time, he must train exactly two students during the first 2-year block and the remaining two during the second 2-year block. Therefore, Acharya Raghunath's training span must be exactly 2 years.

Next, consider Ustad Samiran. We know he never trained more than one student in the same year. Since each of the four students must train under him exactly once, his total training time is the product of his span and the number of students. If his span were 4 years, the total time would be:
$4\text{ students }\times 4\text{ years }=16\text{ years}$
This is impossible within our fixed 12-year window. Because each Guru has a different span, and 2 years is already assigned to Acharya Raghunath, Ustad Samiran's span must be 3 years. This neatly fills the 12-year window continuously since:
$4\times 3=12$
Consequently, the third Guru, Pandit Meghnath, must have the remaining span of 4 years.

Now, let's map out the students under Acharya Raghunath (2-year span). The problem states that in 2013, Ananya started under Pandit Meghnath and Bhaskar started under Ustad Samiran. Because a student cannot train under two Gurus in the same year, neither Ananya nor Bhaskar could train under Acharya Raghunath during his 2013-2014 block. Thus, Charu and Devendra must be the two students who trained under him in 2013-2014. It follows that Ananya and Bhaskar trained under Acharya Raghunath during his 2019-2020 block. This makes Charu and Devendra "Gurubhai" (training under the same Guru at the same time) for exactly 2 years, and Ananya and Bhaskar Gurubhai for exactly 2 years.

Next, let's evaluate Pandit Meghnath's schedule (4-year span). Ananya started under him in 2013, meaning her period was 2013-2016. We know Ananya and Devendra were never Gurubhai, so Devendra cannot overlap with Ananya. We also need Ananya to have a second Gurubhai relationship. The only remaining option for Ananya's Gurubhai is Charu. For Charu to overlap with Ananya for exactly 2 years, Charu must train under Pandit Meghnath from 2015-2018 (overlapping in the years 2015 and 2016).

Finally, we must place Bhaskar and Devendra under Pandit Meghnath (4-year span). Bhaskar trained under Acharya Raghunath in 2019-2020, so he cannot train under Pandit Meghnath during those years. Also, Bhaskar and Charu were never Gurubhai, meaning Bhaskar cannot overlap with Charu's 2015-2018 block. Thus, Bhaskar must train under Pandit Meghnath from 2021-2024. For Devendra to be Gurubhai with Bhaskar for exactly 2 years, without overlapping with Ananya (who ended in 2016) or overlapping with Charu (as Charu ended in 2018, and they cannot be Gurubhai again), Devendra must train under Pandit Meghnath from 2019-2022. This creates an overlap between Devendra (2019-2022) and Bhaskar (2021-2024) exactly during the years 2021 and 2022.

Since Devendra and Bhaskar overlap under Pandit Meghnath in 2021 and 2022, they were Gurubhai during these years. From the given options, the correct year is 2022.