Solution

Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur can be referred to as A, B, C, D respectively and Gurus — Pandit Meghnath, Ustad Samiran, and Acharya Raghunath can be referred as M, S, and R respectively for easy solving. Following table can be drawn to fill Gurus teaching respective musicians in respective years.

Also given info can be marked:

· R does not teach any student during 2015-2018 and 2021-24. This means R can teach only for 2 consecutive years during (2013-2014) and (2019-2020). It can be marked as (~R) in respective years. And since all students need to train under all gurus once, R must be teaching 2 students at the same time (more than 2 students cannot be trained by gurus as per question).

· A and B start training under M and S respectively, but we do not know duration of trainings of these gurus that is fixed for each Guru. So, we can just safely mark for 3 years for A&B as any guru teaches for 2/3/4 years and R trains for 2 years (from above point).

· After marking all this, we know musicians never trained under multiple Gurus in the same year. And A&B are busy with M and S during 2013-2014. So, R must be teaching C&D in 2013-2014.

· A&B must also train under R, but no place is possible for R to train them except 2019-2020. We can fill that as well.

Now, (3^rd)point tells us that except (A,D) and (B,C), all other pairs were Gurubhai, meaning getting trained by same guru simultaneously only for 2 years. The other pairs possible

are (A,B), (A,C), (B,D), (C,D). (1^st)point tells us Gurubhai cannot train under guru S.

· Pair (A,B) have trained as Gurubhai under R during 2019-2020.

· Pair (C,D) have trained as Gurubhai under R during 2013-2014.

· S cannot train Gurubhai, and R’s schedule is already filled, so only M can train the remaining pairs (A,C) and (B,D).

· If S teaches for 4 years, and S cannot train more than 1 student, for S to train all the students, he will require 4*4=16 years, but from 2013-2024 we have only 12 years. Therefore, S can only train for 3 years, teaching all the students in 3*4=12 years. Then, M can teach only in 4 years consecutively.

· B can be trained by M for 4 years consecutively only during 2012-2024. After filling this info,we can see (B,D) to be trained by M simultaneously for 2 years only, is possible only when D trains under M during 2019-2022. This makes (B,D) train together as Gurubhai for 2 years during 2021-2022.

· Pair (A,C) can be trained as Gurubhai by M, only when C is trained by M during 2015-2018. This makes them train as Gurubhai for 2 years during 2015-2016.

· Lastly, S must train both C and A. When S trains A during 2021-2023, then S cannot train C in any year as S can train only 1 musician at a time ( in an year). So S will train A during 2022-2024, so that C can be trained by S during 2019-2021. And D can train under S only during 2016-2018

Q1. A and B were Gurubhai during 2019-2020, so from options, 2020, option(d) will be the answer.

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CAT