Of 60 children, 30 are happy, 10 are sad, and 20 are neither happy nor sad. There are 20 boys and 40 girls. If there are 6 happy boys and 4 sad girls, how many boys are neither happy nor sad?

Answer

To solve the problem step by step, let's break down the information given and calculate the required values.

### Step 1: Identify the total number of children and their categories
We know that:
- Total children = 60
- Happy children = 30
- Sad children = 10
- Neither happy nor sad children = 20

### Step 2: Calculate the total number of boys and girls
From the problem, we have:
- Total boys = 20
- Total girls = 40

### Step 3: Determine the number of happy and sad boys
We are given:
- Happy boys = 6
- Sad girls = 4

### Step 4: Calculate the number of happy girls
Since there are 30 happy children and 6 of them are boys, we can find the number of happy girls:
- Happy girls = Total happy children - Happy boys
- Happy girls = 30 - 6 = 24

### Step 5: Calculate the number of sad boys
We know that there are 10 sad children and 4 of them are girls, so we can find the number of sad boys:
- Sad boys = Total sad children - Sad girls
- Sad boys = 10 - 4 = 6

### Step 6: Calculate the total number of happy and sad boys
Now, we can find the total number of boys who are either happy or sad:
- Total happy and sad boys = Happy boys + Sad boys
- Total happy and sad boys = 6 + 6 = 12

### Step 7: Calculate the number of boys who are neither happy nor sad
To find the number of boys who are neither happy nor sad, we subtract the total number of happy and sad boys from the total number of boys:
- Boys neither happy nor sad = Total boys - Total happy and sad boys
- Boys neither happy nor sad = 20 - 12 = 8

### Final Answer
Thus, the number of boys who are neither happy nor sad is **8**.

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