A group of 1530 persons consisting of captains and soldiers is travelling in a train. For every 14 soldiers there is one captain. The numbers of captains in the group is ______?

105

102

None of these

Let's denote the number of captains as C and the number of soldiers as S.

We know that C + S = 1530.

For every 14 soldiers, there is 1 captain, so S = 14C.

Substitute S = 14C into the first equation:

C + 14C = 1530

15C = 1530

Divide both sides by 15:

C = 102