# ISRO | ISRO CS 2015 | Question 12

A machine needs a minimum of 100 sec to sort 1000 names by quick sort. The minimum time needed to sort 100 names will be approximately
(A) 50.2 sec
(B) 6.7 sec
(C) 72.7 sec
(D) 11.2 sec

Explanation: Best case time complexity of quick sort to take the minimum time to sort names = O(n log n)

```let t1 = time taken to sort 1000 names = 100 sec;
n1=1000 names
let t2 = time taken to sort 100 names;
n2= 100 names

t1/t2 = n1*log(n1) / n2*log(n2)
100/t2 = 1000*log(1000) / 100*log(100)
100/t2 = 10*log(1000) / log(100)
100/t2 = 10*3 / 2
t2 = 20/3 = 6.66 ```

Option (B) is correct

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