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Let a,b,c,ea,b,c,e be positive integer whose average is 2020. Suppose the average of a,b,c,ea,b,c,e is 2626.\newlineWhat is the value of c?c?

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Full solution

Q. Let a,b,c,ea,b,c,e be positive integer whose average is 2020. Suppose the average of a,b,c,ea,b,c,e is 2626.\newlineWhat is the value of c?c?
  1. Calculate Total Sum: First, calculate the total sum of aa, bb, cc, and ee when the average is 2020.\newlineSum = Average ∗* Number of terms\newlineSum = \(20 ∗* 44 = 8080\)
  2. Calculate New Total Sum: Now, calculate the new total sum when the average is increased to 2626. \newlineNew Sum == New Average ∗* Number of terms \newlineNew Sum =26∗4=104= 26 * 4 = 104
  3. Find Difference for Increase: Find the difference between the new sum and the original sum to determine the increase.\newlineIncrease = New Sum - Original Sum\newlineIncrease = 104−80=24104 - 80 = 24
  4. Remainder of aa, bb, and ee: Since the average of aa, bb, and ee remains 2020, their total sum remains the same.\newlineSum of aa, bb, and ee = bb00
  5. Find Value of c: Subtract the sum of aa, bb, and ee from the new total sum to find the value of cc.c=New Sum−Sum of a,b, and ec = \text{New Sum} - \text{Sum of } a, b, \text{ and } ec=104−60=44c = 104 - 60 = 44

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