Directions for question:
In the singing reality show Sa-Re-Ga-Ma-Pa 2018 (Bengali) telecast in the ZEE Bangla Television Channel, five of the contestants made it to the final rounds. They were Ankita, Bablu, Chinmoy, Debarati and Enakshi. The final round would be judged by five eminent Bengali singers and music directors namely Mr Bappi Lahiri, Mr Arijit Singh, Ms Asha Bhosle, Mr Kedar Bhattacharya (Kumar Sanu) and Mr Srikanta Acharya.
Our story is based on the points awarded to the finalists by the judges in the final round.
The following table shows row-wise the number of points given to any three finalists out of the five by a particular judge, the points given being written within brackets beside the name of the finalist. The last right hand column with the heading of ‘ % ’ is the sum of the points earned by the three finalists as a percentage of the sum of the points earned by all the five finalists from the same judge mentioned at the extreme left of the row. All the points given by each judge to the five finalists were distinct, non-negative integers which were multiples of 2.
Judge | Finalists | % | ||
Mr. Bappi Lahiri | Ankita (18) | Bablu (10) | Chinmoy (12) |
80 |
Mr. Arijit Singh | Ankita (8) | Debarati (16) | Enakshi (12) | 90 |
Ms. Asha Bhosle | Chinmoy (22) | Debarati (12) | Enakshi (14) | 80 |
Mr. Kedar Bhattacharya | Ankita (14) | Debarati (16) | Enakshi (4) | 85 |
Mr. Srikanta Acharya | Ankita (6) | Bablu (16) | Chinmoy (10) | 80 |
Question :
If the summation of the total points earned by Bablu and Enakshi was 60, what could be the sum of the total points earned by Chinmoy and Debarati in the final round of Sa-Re-Ga-Ma-Pa 2018 (Bengali) ?
114
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The range of points that could be earned by the finalists individually in the final round of Sa-Re-Ga-Ma-Pa 2018 (Bengali) were :
Ankita : (18+8+2+14+6) to (18+8+10+14+6) = 48 to 56
Bablu : (10+0+2+0+16) to (10+4+10+6+16) = 28 to 46
Chinmoy : (12+0+22+0+10) to (12+4+22+6+10) = 44 to 54
Debarati : (2+16+12+16+0) to (8+16+12+16+8) = 46 to 60
Enakshi : (2+12+14+4+0) to (8+12+14+4+8) = 32 to 46
The summation of the total points earned by Bablu and Enakshi is 60
28+32 = 60
Hence both Bablu and Enakshi had earned the lowest possible number of points of 28 and 32 respectively.
The possibilities of individual points were :
Judge | Ankita | Bablu | Chinmoy | Debarati | Enakshi | Total points |
Mr. Bappi Lahiri | 18 | 10 | 12 | 2,4,6,8 | 8,6,4,2 | 50 |
Mr. Arijit Singh | 8 | 0,4 | 4,0 | 16 | 12 | 40 |
Ms. Asha Bhosle | 2,4,8,10 | 10,8,4,2 | 22 | 12 | 14 | 60 |
Mr. Kedar Bhattacharya | 14 | 0,6 | 6,0 | 16 | 4 | 40 |
Mr. Srikanta Acharya | 6 | 16 | 10 | 0,8 | 8,0 | 40 |
If both Bablu and Enakshi had earned the lowest possible number of points of 28 and 32 respectively, the possibilities of individual points were :
Judge | Ankita | Bablu | Chinmoy | Debarati | Enakshi | Total points |
Mr. Bappi Lahiri | 18 | 10 | 12 | 8 | 2 | 50 |
Mr. Arijit Singh | 8 | 0 | 4 | 16 | 12 | 40 |
Ms. Asha Bhosle | 10 | 2 | 22 | 12 | 14 | 60 |
Mr. Kedar Bhattacharya | 14 | 0 | 6 | 16 | 4 | 40 |
Mr. Srikanta Acharya | 6 | 16 | 10 | 8 | 0 | 40 |
In that case total points earned by Chinmoy = (12+4+22+6+10) = 54
Also total points earned by Debarati = (8+16+12+16+8) = 60
Hence, if the summation of the total points earned by Bablu and Enakshi was 60, what could be the sum of the total points earned by Chinmoy and Debarati in the final round of Sa-Re-Ga-Ma-Pa 2018 (Bengali)
= 54 + 60
= 114