Option A is correct i.e, 400
For sorting 200 names bubble sort makes 200 * 199/2 = 19900 comparisons.So,the time needed for 1 comparison is 200 sec approx.In 800 sec it can make 80,000 comparisons.We have to find n,such that n(n-1)/2=80,000. solving n is approx 400.
200 sec for 200 records
200 <= c * [200]^2
c = 1/200
in 800 sec, records, n = ?
800 <= [1/200]*[n]^2
n = 400
OR
800 is 4 x 200. Bubble sort is O(n*n), so on average you can sort twice as many items in 4 times the time, so the expectation is 400, on average, if 200 was an average case.