Food equivalence (men vs children): A camp has food for 120 men or 200 children (same duration). If 150 children have taken the meal, how many men can be catered with the remaining food?

Introduction / Context:
This problem uses equivalence of consumption between men and children. If total food is sufficient for 120 men (or 200 children) for the same period, we can convert children-consumed food into the “men” equivalent and then subtract from the total men-capacity to find how many men can still be served.

Given Data / Assumptions:

• Total food = capacity for 120 men = capacity for 200 children
• 150 children have eaten
• Consumption rates are constant over the considered period

Concept / Approach:
Equate consumption rates: 120 men ≡ 200 children ⇒ 1 man ≡ 200/120 = 5/3 children ⇒ 1 child ≡ 3/5 man. Convert 150 children to men-equivalents and subtract from 120 to get remaining men-capacity.

Step-by-Step Solution:

Verification / Alternative check:
Children remaining capacity: 200 − 150 = 50 children. Convert 50 children back to men: 50 * 3/5 = 30 men—consistent from either direction.

Why Other Options Are Wrong:

• 56, 45, 36, 27: These do not match the consumption equivalence computed from the given ratio.

Common Pitfalls:
Inverting the equivalence (treating 1 child ≡ 5/3 men) or forgetting that the total food corresponds to the same time period for both groups.

Final Answer:
30