Please solve this

Asked by aastharoy997 | 17th Apr, 2020, 10:50: AM

Expert Answer:

Q: In an examination conducted among 13 students, the average of their score was 60. The top 7 scores have an average of 66 whereas the least 7 scores have an average of 54. Find the 7th highest score.
Solution:
Let the scores of the students be a1, a2, a3, a4, ...., a13 which are arranged in the descending order, which means a1 is the highest and a13 is the lowest.
According to the first condition,
fraction numerator a subscript 1 plus a subscript 2 plus... plus a subscript 13 over denominator 13 end fraction equals 60 space rightwards double arrow a subscript 1 plus a subscript 2 plus... plus a subscript 13 equals 60 cross times 13 space... space left parenthesis i right parenthesis
A c c o r d i n g space t o space t h e space s e c o n d space c o n d i t i o n comma
fraction numerator a subscript 1 plus a subscript 2 plus... plus a subscript 7 over denominator 7 end fraction equals 66 space rightwards double arrow a subscript 1 plus a subscript 2 plus... plus a subscript 7 equals 66 cross times 7 space space rightwards double arrow space a subscript 1 plus a subscript 2 plus... plus a subscript 6 space equals 66 cross times 7 minus a subscript 7... space left parenthesis i i right parenthesis
A c c o r d i n g space t o space t h e space s e c o n d space c o n d i t i o n comma
fraction numerator a subscript 7 plus a subscript 8 plus... plus a subscript 13 over denominator 7 end fraction equals 54 space rightwards double arrow a subscript 7 plus a subscript 8 plus... plus a subscript 13 equals 54 cross times 7 space space rightwards double arrow space a subscript 8 plus... plus a subscript 13 space equals 54 cross times 7 minus a subscript 7 space... space left parenthesis i i i right parenthesis
S u b s t i t u t i n g space left parenthesis i i right parenthesis space a n d space left parenthesis i i i right parenthesis space i n space left parenthesis i right parenthesis comma space w e space h a v e
open parentheses 66 cross times 7 minus a subscript 7 close parentheses plus a subscript 7 plus open parentheses 54 cross times 7 minus a subscript 7 close parentheses equals 60 cross times 13
rightwards double arrow 66 cross times 7 plus 54 cross times 7 minus a subscript 7 equals 60 cross times 13
rightwards double arrow open parentheses 66 plus 54 close parentheses cross times 7 minus a subscript 7 equals 60 cross times 13
rightwards double arrow 120 cross times 7 minus 60 cross times 13 equals a subscript 7
rightwards double arrow a subscript 7 equals 840 minus 780 equals 60
H e n c e comma space t h e space 7 to the power of t h end exponent space h i g h e s t space s c o r e space i s space 60.

Answered by Renu Varma | 17th Apr, 2020, 12:05: PM