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 ______?
- 90
- 105
- 102
- None of these
Explanation
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
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