In a garden there are a total of 361 saplings consisting only of mango tree saplings and neem tree saplings. The ratio of the number of mango saplings to the number of neem saplings is 11 : 8. How many mango tree saplings are there in the garden?

Introduction / Context:
This problem is a straightforward application of ratios in a real life setting. We are given the total number of saplings in a garden and the ratio between two types of trees, mango and neem. The goal is to convert the ratio into actual numbers that add up to the total. Such questions are very common in aptitude tests because they check a candidate understanding of basic ratio and proportion ideas.

Given Data / Assumptions:

• Total number of saplings (mango plus neem) = 361.
• Ratio of mango saplings to neem saplings = 11 : 8.
• Let mango saplings be represented by 11 parts and neem saplings by 8 parts.
• We assume that no other type of tree is present in the garden.

Concept / Approach:
If two quantities are in the ratio a : b, then they can be written as a * k and b * k, where k is a common multiplier. The sum of the parts a + b multiplied by k gives the total. Therefore, we find k by dividing the total quantity by the sum of the ratio parts. Once k is known, individual quantities are easily obtained by multiplication. This is a core property of ratios and proportions that appears in many competitive exams.

Step-by-Step Solution:
Let the number of mango saplings be 11k and the number of neem saplings be 8k. Total number of saplings = 11k + 8k = 19k. We are told that 19k = 361. So k = 361 / 19. Compute 361 / 19 = 19. Therefore, number of mango saplings = 11k = 11 * 19 = 209. Number of neem saplings = 8k = 8 * 19 = 152 (this also checks that 209 + 152 = 361).

Verification / Alternative check:
We can check the ratio directly. If there are 209 mango saplings and 152 neem saplings, their ratio is 209 : 152. Both numbers are divisible by 19, which gives 209 / 19 = 11 and 152 / 19 = 8. So the simplified ratio is 11 : 8, which matches the given condition. Also, the sum 209 + 152 equals 361, confirming that the total saplings count is maintained.

Why Other Options Are Wrong:
171 would require the remaining 190 saplings to be neem, giving a ratio 171 : 190, which does not simplify to 11 : 8. 57 would imply 304 neem saplings, and 57 : 304 does not match the required ratio. 152 is the number of neem saplings, not mango, so it answers the wrong quantity. 190 also leads to a mismatch when compared with the ratio 11 : 8.

Common Pitfalls:
A frequent mistake is to try to guess numbers that add to 361 without respecting the ratio. Another error is to treat 11 and 8 as percentages and directly use them on the total, which is not correct. Always remember that ratio parts are relative units, not percentages. The correct method is to sum the ratio parts, divide the total by this sum to find the value of one part, and then multiply by individual ratio numbers.

Final Answer:
The garden contains 209 mango tree saplings.