In a camp there is enough meal to feed either 120 men or 200 children for one meal. If 150 children have already taken their meal, how many men can still be catered with the remaining meal supply?

Introduction:
This question illustrates a typical chain rule or proportion concept involving equivalent consumption of resources by men and children. The key idea is that the total quantity of meal is fixed, and the meal that can feed a certain number of children can be converted into an equivalent number of men based on the given ratios.

Given Data / Assumptions:
Total meal is sufficient for 120 men. The same meal is also sufficient for 200 children. 150 children have already taken the meal. We assume each man and each child consumes a fixed amount of meal per person. We need to find how many men can be fed with the remaining meal.

Concept / Approach:
Since the same meal can feed 120 men or 200 children, the total quantity of meal can be expressed in man meals or child meals. We can first work in terms of children. After 150 children have eaten, we find how many children equivalent meals remain. Then we convert that remaining quantity into an equivalent number of men using the ratio between men and children consumption.

Step-by-Step Solution:
Step 1: Treat the entire meal as 200 child meals. Total capacity = 200 children (for one meal). Step 2: Subtract the consumption of 150 children. Children already fed = 150. Remaining child meals = 200 − 150 = 50 child meals. Step 3: Relate child meals to man meals using the given information. 120 men are equivalent to 200 children. So 1 child meal = 120 / 200 man meals = 3 / 5 man meals. Step 4: Convert remaining child meals to man meals. Remaining man meals = 50 * (3 / 5) = 30 man meals. Therefore, 30 men can be fully fed with the remaining meal.

Verification / Alternative check:
We can also express the total meal in man meals. Since 120 men can be fed, total capacity is 120 man meals. One man meal = 200 / 120 child meals = 5 / 3 child meals. If 150 children have eaten, that is 150 child meals, which equals 150 * (3 / 5) = 90 man meals. Remaining man meals = 120 − 90 = 30, confirming the same result.

Why Other Options Are Wrong:
50 men would require 50 man meals, which is more than the 30 man meals left. 40 and 20 men do not match the equivalence calculation when we convert remaining child meals into man meals. 10 men underutilise the available food, since the remaining quantity is enough for 30 men.

Common Pitfalls:
Many learners confuse the ratio and try to use direct proportion incorrectly, such as treating men and children as interchangeable without a conversion factor. Another common mistake is subtracting 150 directly from 120 or 200 without recognising that we must convert between child meals and man meals properly. Always convert the total resource into one consistent unit first and then perform the calculations.

Final Answer:
With the remaining meal, the camp can still cater to 30 men.