G.P Actual Question in XAT 2022

Q. Shireen draws a circle in her courtyard. She then measures the circle’s circumference and its diameter with her measuring tape and records them as two integers, A and B respectively. She finds that A and B are co primes, that is, their greatest common divisor is 1. She also finds their ratio, A:B, to be:3.141614161416… (repeating endlessly).
What is A – B ?
A 21414
B 7138
C 21417
D 21413
E 15

EXPLANATION

.B
We have
3.1416141614161416……

Now excluding 3 we get a series with infinite Geometric progression such that first term is

and common ratio is

Therefore we get sum as a/1-r

Now adding 3 we get value as :

Now taking 3 common we get ratio of A:B as