Let x =First odd Number
Sum of 4 consecutive two digit odd numbers = x + x + 2 + x + 4 + x + 6 = 4x + 12
Let y= $(\frac{4x+12}{10})^{\frac{1}{2}}$
$\frac{4x+12}{10}=y^{2}$
$\frac{2x+6}{5}$=$y^{2}$
There are only 9 choice (17,27,37,47,57,67,77,87,97) are possible for the valve of x.
From the help of given options we can eliminate (27,47,57,77,87,97).
now check for remaining (17,37,67) choices.
put x=17
$\frac{40}{5}=8$
Here 8 is not a perfect square. so can elimate Option (1) and (2) from here.
now put x=67
$\frac{140}{5}=28$
Here 67 is not a perfect square. so can elimate Option (4) and (5) from here.
Now put x=37
$\frac{80}{5}=16$
Here 16 is a perfect square.
and four consecutive two digit odd numbers x =37
x + 2=39
x + 4 =41
x + 6 =43
Hence (3)41 is the correct choice.