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 Ananya and Bhaskar Gurubhai?

The correct option is 2020.

To determine the years in which Ananya and Bhaskar were Gurubhai, we need to analyze the training periods and the availability of the Gurus step-by-step. Let us define the four musicians as Ananya, Bhaskar, Charu, and Devendra, and the three Gurus as Pandit Meghnath, Ustad Samiran, and Acharya Raghunath.

First, we determine the training span for Acharya Raghunath. According to Fact 2, Acharya Raghunath did not train any students during the years 2015 to 2018, as well as during 2021 to 2024. The total period under consideration is from 2013 to 2024. By removing the restricted years, Acharya Raghunath is only available to train students during two isolated time windows:
1. 2013 and 2014
2. 2019 and 2020

We are given that each Guru trains any student for a continuous span of exactly 2, 3, or 4 years, and each Guru has a different span. Because Acharya Raghunath only has 2-year continuous windows available, his training span must be exactly 2 years.

Next, we know every student must start and complete their training under each of the three Gurus. Therefore, Acharya Raghunath must train all four students. However, the problem states that no Guru can train more than two students at the same time. This means Acharya Raghunath must train exactly two students during his 2013-2014 window, and the remaining two students during his 2019-2020 window.

Now, let us look at Fact 4. In 2013, Ananya started her training under Pandit Meghnath, while Bhaskar started his training under Ustad Samiran. Because a student cannot train under multiple Gurus in the same year, neither Ananya nor Bhaskar could have trained under Acharya Raghunath during his 2013-2014 window.

By elimination, the two students who trained under Acharya Raghunath during 2013-2014 must be Charu and Devendra. Consequently, Ananya and Bhaskar must have completed their 2-year training under Acharya Raghunath during the only other available window: 2019 and 2020.

The problem defines "Gurubhai" as two students training under the same Guru at the same time. Since both Ananya and Bhaskar were training together under Acharya Raghunath during 2019 and 2020, they were Gurubhai in both of these years. Furthermore, Fact 3 states that Ananya and Bhaskar were Gurubhai for exactly 2 years in total, meaning these are the only two years they shared this status.

Looking at the given options (2020, 2018, 2021, 2024), the year 2020 is when Ananya and Bhaskar were Gurubhai.