A group of 1200 persons consisting of captains and soldiers is travelling in a train. If for every 15 soldiers there is one captain, then the number of captains in the group is

### Concept & Strategy Treat the ratio of soldiers to captains as a single cohesive unit. Find the size of one complete unit and divide the total population by this unit size to find the number of groups (and thus, captains). $$Total\ Groups = \frac{Total\ Population}{Size\ of\ One\ Group}$$ ### Step-by-Step Solution * **Given:** * Total persons = 1200 * Ratio = 15 soldiers for every 1 captain * **Calculation:** 1. Determine the size of a single complete unit (group): $15\ soldiers + 1\ captain = 16\ persons\ per\ unit$ 2. Divide the total number of people by the size of one unit to find how many such units exist: $1200 / 16 = 75\ units$ 3. Since there is exactly 1 captain per unit, the total number of captains is equal to the number of units. $Captains = 75 \times 1 = 75$ ### Exam Strategy & Shortcut Recognize the combined ratio immediately. 15 to 1 means the total must be divided by 16. To divide 1200 by 16 quickly mentally: Divide by 4 twice. $1200 / 4 = 300$. $300 / 4 = 75$. ### Common Pitfall The most prevalent error is dividing the total number of persons (1200) directly by the number of soldiers (15), yielding 80. Option (c) is a trap designed specifically for this mistake. Always divide the total by the *sum* of the ratio components. ### Final Answer **Therefore, the correct answer is 75.**