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

Which of the following statements is TRUE?

The correct answer is: Charu was training under Ustad Samiran in 2019.

To arrive at this conclusion, we need to carefully map out the training schedules for all four musicians (Ananya, Bhaskar, Charu, and Devendra) based on the strict chronological constraints provided in the problem. Let's break down the logic step-by-step.

Step 1: Determine the training spans for each Guru
We know the total duration of the timeline spans from 2013 to 2024 inclusive, which is exactly 12 years. Additionally, each Guru has a unique and fixed training span of 2, 3, or 4 consecutive years.

First, consider Acharya Raghunath (AR). We are told he did not train students during 2015-2018 and 2021-2024. This means he only actively trained students in two distinct windows: 2013-2014 and 2019-2020. Because these are exactly two independent 2-year blocks, and he needs to train all 4 students (taking a maximum of 2 at a time), his training span must be exactly 2 years.

Next, consider Ustad Samiran (US). The rules state he never trains more than one student at a time. To train all 4 students sequentially within the 12-year timeframe without overlapping, his span multiplied by 4 must be less than or equal to 12. Since the 2-year span is already taken by AR, US's span must be 3 years.

$4\times 3=12$

This tells us that Ustad Samiran is occupied for the entire 12-year duration, divided perfectly into four continuous 3-year blocks: 2013-2015, 2016-2018, 2019-2021, and 2022-2024.

Consequently, by process of elimination, Pandit Meghnath (PM) must take the remaining training span of 4 years.

Step 2: Assign Initial Timelines
We are given explicit starting facts for the year 2013:
- Bhaskar starts under US. With a 3-year span, Bhaskar's training under US runs from 2013 to 2015.
- Ananya starts under PM. With a 4-year span, Ananya's training under PM runs from 2013 to 2016.

Step 3: Deduce Acharya Raghunath's (AR) Students
AR's first available 2-year window is 2013-2014. Since Ananya and Bhaskar are already actively training under PM and US respectively during these exact years, they cannot train under AR at this time. Therefore, the two students training under AR during 2013-2014 must be Charu and Devendra.

Because each student must train under each Guru, this leaves AR's second available window, 2019-2020, exclusively for Ananya and Bhaskar.

Step 4: Map out the "Gurubhai" Pairings
"Gurubhais" are students training under the same Guru at the same exact time. Based on Step 3, we have successfully identified two pairs of Gurubhais under AR: Charu & Devendra (2013-2014) and Ananya & Bhaskar (2019-2020).

The problem reveals that Ananya & Devendra, and Bhaskar & Charu were NEVER Gurubhai. This means the only remaining valid pairs that must be Gurubhai for exactly 2 years are Ananya & Charu, and Bhaskar & Devendra. Because US trains students completely alone, these specific overlapping pairings must occur under PM.

Let's map the overlap for Ananya & Charu:
Ananya is with PM from 2013-2016. For Charu to overlap with her for exactly 2 years, Charu must train under PM from 2015-2018. This creates a valid 2-year overlap during 2015-2016. (Charu is free to do this since her AR training ended in 2014).

Let's map the overlap for Bhaskar & Devendra:
Bhaskar is busy with AR until 2020. His 4-year PM training must therefore be 2021-2024. For Devendra to overlap with him for exactly two years, Devendra's PM training must be 2019-2022. This creates a valid 2-year overlap during 2021-2022.

Step 5: Fill in Ustad Samiran's (US) Schedule
US still needs to train Devendra, Charu, and Ananya during the three remaining open blocks: 2016-2018, 2019-2021, and 2022-2024.
- Devendra is busy during 2013-2014 (AR) and 2019-2022 (PM). The only US window that fits his schedule is 2016-2018.
- Charu is busy during 2013-2014 (AR) and 2015-2018 (PM). The only US window that fits her schedule is 2019-2021.
- Ananya is busy during 2013-2016 (PM) and 2019-2020 (AR). The only US window that fits her schedule is 2022-2024.

Conclusion
By carefully tracking the 3-year timeline for Ustad Samiran, we deduced that Charu was assigned to the 2019-2021 block. Therefore, the statement explicitly asserting that Charu was training under Ustad Samiran in 2019 is undeniably true, matching our derived logical constraints perfectly.