There is certain numbers of toys in the box. They are divided into such a way that the person who gets 1/4 of the whole gets thrice of what others get on an average.

Options

A. 8
B. 10
C. 12
D. 9

Answer

To solve the problem, we need to analyze the information given and set up an equation based on the ratios described. Let's break it down step by step.

### Step 1: Define Variables
Let the total number of toys be \( T \). According to the problem, one person receives \( \frac{1}{4} \) of the total toys, which means this person receives:
\[ \text{Toys received by one person} = \frac{1}{4} T \]

### Step 2: Determine the Remaining Toys
The remaining toys after one person has taken \( \frac{1}{4} \) of the total are:
\[ \text{Remaining toys} = T - \frac{1}{4} T = \frac{3}{4} T \]

### Step 3: Define the Number of Other People
Let the number of other people be \( n \). Therefore, the average number of toys each of these \( n \) people receives is:
\[ \text{Average toys per other person} = \frac{\frac{3}{4} T}{n} = \frac{3T}{4n} \]

### Step 4: Set Up the Equation
According to the problem, the person who receives \( \frac{1}{4} T \) gets three times what each of the other \( n \) people gets on average. Thus, we can set up the equation:
\[ \frac{1}{4} T = 3 \left( \frac{3T}{4n} \right) \]

### Step 5: Simplify the Equation
Now, simplify the equation:
\[ \frac{1}{4} T = \frac{9T}{4n} \]
To eliminate \( T \) from both sides (assuming \( T \neq 0 \)):
\[ \frac{1}{4} = \frac{9}{4n} \]

### Step 6: Cross-Multiply
Cross-multiply to solve for \( n \):
\[ 1 \cdot 4n = 9 \cdot 4 \]
\[ 4n = 9 \]

### Step 7: Solve for \( n \)
Now, divide both sides by 4:
\[ n = \frac{9}{4} \]
Since \( n \) must be a whole number, we realize that there must be an error in our interpretation.

### Step 8: Re-evaluate the Problem
The person receiving \( \frac{1}{4} T \) should be considered as one of the total people. Therefore, the total number of people \( N \) is:
\[ N = n + 1 \]
Thus:
\[ n = 3 \Rightarrow N = 3 + 1 = 4 \]

### Final Answer
The total number of people is \( 4 \).

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