Captains and soldiers on a train — total people = 1200. For every 15 soldiers, there is 1 captain. How many captains are there?

Introduction / Context:
This ratio-and-total problem converts a “for every” statement into a part–whole composition. Each “group” contains a fixed number of soldiers and one captain. Count how many such groups fit into the total to get the number of captains.

Given Data / Assumptions:

• Total people = 1200.
• For each captain there are 15 soldiers.
• One group = 15 soldiers + 1 captain = 16 people.

Concept / Approach:
Let C = number of captains. Then Soldiers S = 15C. Total = S + C = 15C + C = 16C. Solve 16C = 1200. This directly yields the captain count.

Step-by-Step Solution:

Verification / Alternative check:
Check group counts: 75 groups of 16 equals 1200. The 15:1 soldier-to-captain ratio is preserved (1125:75 = 15:1).

Why Other Options Are Wrong:

• 85, 80, 70 — do not satisfy 16C = 1200 and would give incorrect totals.

Common Pitfalls:
Using 15 as the divisor instead of 16; remember that each group includes the captain as well as soldiers.

Final Answer:
75