𝐒𝟏 is a series of five consecutive multiples of 4 whose sum is 100. 𝐒𝟐 is a series of 4 consecutive even integers such that the second smallest number of 𝐒𝟐 is 6 less than largest number of 𝐒𝟏. Find average of series 𝐒𝟐.

The correct option is 23.

Let us solve the problem step-by-step.

Step 1: Understand and find the numbers in series S₁

Series S₁ consists of 5 consecutive multiples of 4.
Let the middle number (3^rd number) of S₁ be $x$.
Since the numbers are consecutive multiples of 4, the 5 numbers can be written as:

$(x-8),(x-4),x,(x+4),(x+8)$

We are given that the sum of series S₁ is 100:

$(x-8)+(x-4)+x+(x+4)+(x+8)=100$

$5x=100$

$x=20$

The largest number of series S₁ is:

$x+8=20+8=28$

Step 2: Understand and find the numbers in series S₂

Series S₂ consists of 4 consecutive even integers.
Let the 4 consecutive even integers be $y,y+2,y+4,y+6$.

The second smallest number of S₂ is $y+2$.
We are given that the second smallest number of S₂ is 6 less than the largest number of S₁ (which is 28):

$y+2=28-6$

$y+2=22$

$y=20$

Thus, the 4 consecutive even numbers of series S₂ are:

20, 22, 24, and 26.

Step 3: Calculate the average of series S₂

The average of these 4 numbers is:

$\text{Average}=\frac{20+22+24+26}{4}$

$\text{Average}=\frac{92}{4}=23$

Hence, the average of series S₂ is 23.