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 ofthe missing numbers(a and b) is:

Given numbers are 24, 45, a, 35, 59, 83, 46, b, 29, 74

Each number is added to its serial number, then the average of the new numbers formed is 55

Sum of the numbers = 55 x 10 = 550

$$=$$>  $$\left(24+1\right)+\left(45+2\right)+\left(a+3\right)+\left(35+4\right)+\left(59+5\right)+\left(83+6\right)+\left(46+7\right)+\left(b+8\right)+\left(29+9\right)+\left(74+10\right)=550$$

$$=$$>  $$24+45+a+35+59+83+46+b+29+74+\left(1+2+....+10\right)=550$$

$$=$$>  $$395+a+b+\frac{10\left(10+1\right)}{2}=550$$

$$=$$>  $$395+a+b+55=550$$

$$=$$>  $$450+a+b=550$$

$$=$$>  $$a+b=100$$

$$=$$>  $$\frac{a+b}{2}=50$$

$$\therefore\ $$Average of a and b = 50

Hence, the correct answer is Option C