Correct Answer  Option 3 : 73.11
Concept:
Radioactive decay

Radioactivity: The atoms having a number of neutrons much more than proton are unstable. The nuclei of such atoms exhibit radioactivity.
 An example of Such an Atom is U  238, where the number of Neutrons is 146, and the number of protons is 92.
 Radium is an important radioactive atom.

Radioactive decay: The spontaneous breakdown of such an unstable atomic nucleus causes radioactivity.
 The process of radioactive decay as a function of time is represented by
\(ln (\frac{N}{N_0}) =  λ t\)
N is the number of radioactive nuclei present in a sample, No is the number of radioactive nuclei present in the sample at t = 0, λ is disintegration constant.

Disintegration constant: The disintegration constant is the unique constant related to the radioactive nature of the given nucleus.

HalfLife Period: The time in which the number of nuclei reached to half of its initial value is called the halflife period.
It is the time period when N = N0 / 2
The half  Life period is given as
\(ln (\frac{N_0 /2}{N_0}) =  λ t_{1/2}\)
⇒ \(t_{1/2} = \frac{ln2}{λ}\)
Calculation:
Given halflife is 22 years
\(\implies 22 = \frac{ln2}{λ}\)
\(\implies \lambda = \frac{ln2}{22}\)  (1)
Now, we got the value of disintegration constant.
It is given that the substance is decreased to 10 %
So, N = 10 % of N_{o}
Or
\(\frac{N}{N_0} = \frac{1}{10}\)  (2)
We know that
\(ln (\frac{N}{N_0}) =  λ t\)
Using (1) and (2) in the above equation
\(\implies ln (\frac{1}{10}) =  \frac{ln 2}{22} t\)
\(\implies  ln \ 10 =  \frac{ln 2}{22} t\)
\(\implies t = \frac{ln 10}{ln 2} \times 22\)
⇒ t = 73.11 years.
So, the correct option is 73.11 years