In a hospital there are 209 doctors and nurses together. If the ratio of the number of doctors to the number of nurses is 11 : 8, how many nurses are there in the hospital?

Introduction / Context:
This is a simple ratio and total problem involving staff in a hospital. We are told how many doctors and nurses there are in total and given the ratio of doctors to nurses. From this information, we can determine the exact number of doctors and nurses separately. Such questions are common in aptitude tests and help reinforce the idea that ratios can be converted to actual counts when the total is known.

Given Data / Assumptions:
- Total number of doctors and nurses together is 209.
- Ratio of doctors to nurses is 11 : 8.
- Let doctors be the first term and nurses be the second term of the ratio.
- We need the number of nurses only.

Concept / Approach:
If the ratio of doctors to nurses is 11 : 8, we can assume there are 11k doctors and 8k nurses for some positive number k. Their sum is 11k + 8k which is 19k. Since the total is given as 209, we can solve 19k = 209. Once k is found, we multiply it by 8 to get the number of nurses and by 11 to get the number of doctors if needed.

Step-by-Step Solution:
Step 1: Let number of doctors = 11k and number of nurses = 8k. Step 2: Total staff = 11k + 8k = 19k. Step 3: Given total staff = 209, so 19k = 209. Step 4: Solve for k: k = 209 / 19. Step 5: Compute 209 / 19 = 11. Step 6: Number of nurses = 8k = 8 * 11 = 88.

Verification / Alternative check:
To verify, calculate the number of doctors as 11k = 11 * 11 = 121. Add doctors and nurses to get 121 + 88 = 209, which matches the given total. Also, the ratio 121 : 88 simplifies to 11 : 8 when both terms are divided by 11, confirming that the allocation is correct.

Why Other Options Are Wrong:
96, 108 and 121 do not satisfy both conditions simultaneously. For example, if nurses were 96 and doctors were 209 minus 96 which is 113, the ratio 113 : 96 does not reduce to 11 : 8. Similarly, other assumed nurse counts fail to yield the target ratio and total. Only 88 nurses with 121 doctors perfectly fit the ratio and sum conditions.

Common Pitfalls:
One common mistake is to reverse the ratio and treat nurses as the first term and doctors as the second term, which leads to wrong numbers. Another error is miscalculating k by dividing 209 by something other than the sum of the ratio terms 19. Careful identification of which group corresponds to which part of the ratio is essential.

Final Answer:
The number of nurses in the hospital is 88.