**Given:**

- The camp had enough food to last for 50 days for 2200 soldiers.
- After 17 days, some more soldiers joined the camp.
- The remaining food lasted for 20 more days.

**To find:**

- The number of soldiers who joined the camp later.

**Assumptions:**

- The rate of consumption of food remains constant throughout the duration.
- The number of soldiers joining the camp later is the same every day.
- The initial number of soldiers is 2200.

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**Solution:**

Let's assume the rate of consumption of food per soldier per day is "x".

Therefore, the total amount of food available initially is given by:
Initial food quantity = 50 * 2200 * x

After 17 days, the remaining food quantity is given by:
Remaining food quantity = 33 * 2200 * x

Since the remaining food lasted for 20 more days, the total food quantity is the same. Hence, we can equate the two:

50 * 2200 * x = 33 * 2200 * x

Simplifying the equation, we get:
50 = 33

This implies that the rate of consumption of food per soldier per day, x, is equal to zero. However, this is not possible as it would mean the soldiers did not consume any food.

Hence, our assumption that the rate of consumption remains constant throughout the duration is incorrect.

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**Revised Solution:**

Let's assume that the rate of consumption of food per soldier per day is not constant and varies with the number of soldiers.

Let the initial number of soldiers be N. Therefore,

Initial food quantity = 50 * N * x

After 17 days, the remaining food quantity is given by:
Remaining food quantity = 33 * N * x

The remaining food lasted for 20 more days. Therefore, the remaining food quantity is given by:
Remaining food quantity = 20 * (N + M) * x

where M is the number of soldiers who joined the camp later.

Since the remaining food quantity is the same, we can equate the two:

33 * N * x = 20 * (N + M) * x

Simplifying the equation, we get:
33N = 20(N + M)

Expanding the equation, we get:
33N = 20N + 20M

Simplifying further, we get:
13N = 20M

Therefore, the number of soldiers who joined the camp later is given by:
M = (13N) / 20

Now, we need to find a value for N that satisfies the given conditions.

Since the initial food quantity is enough to last for 50 days for 2200 soldiers, we can calculate the rate of consumption per soldier per day:

x = Initial food quantity / (50 * N) = 2200 / 50

Using this value of x, we can substitute it into the equation for M to find the number of soldiers who joined the camp later.

M = (13N) / 20

Finally, we can substitute the value of N into the equation to find the value of M, which represents the number of soldiers who joined the camp later.

Use ratio