What will come in the place of question (?) mark in the following number series.

80, ?, 117, 168, 271, 478

The correct option is 92.

To find the missing number in the given series, let us analyze the differences between consecutive terms:

Given series: 80, ?, 117, 168, 271, 478

First, let us calculate the differences between the known adjacent numbers:

Difference between 478 and 271:

$478-271=207$

Difference between 271 and 168:

$271-168=103$

Difference between 168 and 117:

$168-117=51$

Now, let us examine the pattern in these differences (207, 103, 51):

$207=2\times 103+1$

$103=2\times 51+1$

Following this reverse pattern, if $d_n=2\times d_{n-1}+1$, then the previous difference $d_{n-1}$ can be obtained using:

$d_{n-1}=\frac{d_n-1}{2}$

Let us calculate the preceding differences:

Difference before 51 (between 117 and ?):

$\frac{51-1}{2}=25$

Difference before 25 (between ? and 80):

$\frac{25-1}{2}=12$

Now, applying these differences step-by-step from left to right:

First term = 80

Second term (?) = $80+12=92$

Third term = $92+25=117$

Fourth term = $117+51=168$

Fifth term = $168+103=271$

Sixth term = $271+207=478$

Thus, the number that replaces the question mark (?) is 92.