Average problem 4 by Dhaval Furia

Algebra Level pending

Ramesh and Gautam are among 22 22 students who write an examination. Ramesh scores 82.5 82.5 . The average score of the 21 21 students other than Gautam is 62 62 . The average score of all the 22 22 students is one more than the average score of the 21 21 students other than Ramesh . The score of Gautam is _____

48 48 53 53 51 51 49 49

Dhaval Furia by Dhaval Furia , 26, India

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1 solution

Let the score of Gautam be G G , sum of scores of students except Ramesh and Gautam be S 20 = 62 × 21 − 82.5 = 1219.5 S_{20}=62\times 21-82.5=1219.5 . Then

62 × 21 + G 22 = 1 + S 20 + G 21 \dfrac{62\times 21+G}{22}=1+\dfrac{S_{20}+G}{21}

⟹ G = 1302 × 21 − 22 × 21 − 22 × 1219.5 = 51 \implies G=1302\times 21-22\times 21-22\times 1219.5=\boxed {51} .

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