There are 361 saplings of Mango and Neem in a garden. The ratio of the number of Mango saplings to that of Neem saplings is 8 : 11. How many Neem saplings are there in the garden?
209
Finding the Number of Neem Saplings Using Ratios
This problem involves understanding and applying ratios to find the number of Neem saplings in a garden, given the total number of saplings and the ratio of Mango to Neem saplings.
Understanding the Sapling Ratio
The ratio of Mango saplings to Neem saplings is given as 8 : 11. This ratio means that for every 8 Mango saplings, there are 11 Neem saplings. The ratio tells us the proportion of each type of sapling relative to the total number of saplings.
Calculating Total Ratio Parts
To work with the ratio and the total number of saplings, we first need to find the total number of parts in the ratio. We do this by adding the numbers in the ratio:
Total ratio parts = Ratio of Mango parts + Ratio of Neem parts
Total ratio parts = \(8 + 11 = 19\)
So, the total number of saplings (361) is divided into 19 equal parts.
Determining the Value of One Ratio Part
Now we can find out how many saplings each ratio part represents. We divide the total number of saplings by the total number of ratio parts:
Value of one ratio part = Total saplings / Total ratio parts
Value of one ratio part = \(\frac{361}{19}\)
Performing the division:
\(361 \div 19 = 19\)
So, each ratio part represents 19 saplings.
Calculating the Number of Neem Saplings
The ratio of Neem saplings is 11. Since each ratio part is equal to 19 saplings, the number of Neem saplings is found by multiplying the Neem ratio part by the value of one ratio part:
Number of Neem saplings = Neem ratio part × Value of one ratio part
Number of Neem saplings = \(11 \times 19\)
Calculating the product:
\(11 \times 19 = 209\)
Therefore, there are 209 Neem saplings in the garden.
Verification
We can also find the number of Mango saplings to verify our calculation. The Mango ratio part is 8.
Number of Mango saplings = Mango ratio part × Value of one ratio part
Number of Mango saplings = \(8 \times 19\)
\(8 \times 19 = 152\)
Total saplings = Number of Mango saplings + Number of Neem saplings
Total saplings = \(152 + 209 = 361\)
This matches the total number of saplings given in the problem, confirming our calculation is correct.
| Item | Ratio Part | Number of Saplings |
|---|---|---|
| Mango Saplings | 8 | \(8 \times 19 = 152\) |
| Neem Saplings | 11 | \(11 \times 19 = 209\) |
| Total Saplings | 19 | \(152 + 209 = 361\) |
Revision Table: Understanding Ratios and Proportions
| Concept | Description | Application in this Problem |
|---|---|---|
| Ratio | A comparison of two or more quantities of the same kind. Expressed as a : b. | The ratio of Mango to Neem saplings is 8 : 11. |
| Total Ratio Parts | The sum of the numbers in the ratio. Represents the total "units" the whole is divided into. | \(8 + 11 = 19\) total parts. |
| Value of One Part | The total quantity divided by the total ratio parts. Determines the value of each unit. | \(361 \div 19 = 19\) saplings per part. |
| Finding Quantity | Multiply the ratio part for a specific item by the value of one part. | Neem saplings: \(11 \times 19 = 209\). Mango saplings: \(8 \times 19 = 152\). |
Additional Information: Solving Ratio Problems
Ratio problems often involve finding the quantities of individual components when the total quantity and the ratio are known. Here are the general steps:
- Step 1: Understand the ratio given. Identify what quantities the ratio represents.
- Step 2: Calculate the total number of parts in the ratio by adding the individual ratio components.
- Step 3: Find the value of one ratio part by dividing the total given quantity by the total number of ratio parts.
- Step 4: Calculate the quantity of each component by multiplying its respective ratio part by the value of one ratio part.
- Step 5: Verify your answer by adding the calculated quantities of all components. The sum should equal the total quantity given in the problem.
This method can be applied to various problems involving dividing a total amount according to a given ratio, such as distributing money, mixing ingredients, or calculating proportions of different items in a collection.
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