the numbers 24,45,a,35,59,83,46,b,29,74 are serially numbered as they appear in the sequence. When each number is added to its serial number, then the average of the new numbers formed is 55. The average of the missing numbers a and b is :

Question

Answer 1

Hint -> add serial number to every number
like 24+1 , 45+2,a+3,....74+10 -> 395+(1+2...10)+a+b

Sum of First N natural numbers n(n+1)/2
sum of First 10 Natural Numbers 10(11)/2 = 55

Now avg =( 395+55+a+b)/10 = 55
a+b = 100
average of a and b is 100/2 = 50

Answer 2

Hint -> add serial number to every number
like 24+1 , 45+2,a+3,....74+10 -> 395+(1+2...10)+a+b

Sum of First N natural numbers n(n+1)/2
sum of First 10 Natural Numbers 10(11)/2 = 55

Now avg =( 395+55+a+b)/10 = 55
a+b = 100
average of a and b is 100/2 = 50

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the numbers 24,45,a,35,59,83,46,b,29,74 are serially numbered as they appear in the sequence. When each number is added to its serial number, then the average of the new numbers formed is 55. The average of the missing numbers a and b is :