Once I met two persons of the same parents namely Ashmit and Amish. Mean while Ashmit told me that he has twic the number of sisters as the number of brothers. Further Amisha told me that he has twice the number of sisters as the number of brothers. Furtger Amisha told me that she has twice the number of brothers are the number of sisters. Actually it was very confusing for me, so do you know that how many brothers and sisters are in their family?

Options

A. a. 4
B. b. 5
C. c. 6
D. d. can't be determined

Answer

To solve the problem of how many brothers and sisters are in Ashmit and Amisha's family, we can break it down step by step.

### Step 1: Define Variables
Let:
- \( B \) = number of brothers
- \( S \) = number of sisters

### Step 2: Analyze Ashmit's Statement
Ashmit states that he has twice the number of sisters as the number of brothers. Since Ashmit himself is one of the brothers, we can express this as:
\[ S = 2(B - 1) \]
This means the number of sisters \( S \) is twice the number of brothers excluding Ashmit.

### Step 3: Analyze Amisha's Statement
Amisha states that she has twice the number of brothers as the number of sisters. Since Amisha is a sister, we can express this as:
\[ B = 2(S - 1) \]
This means the number of brothers \( B \) is twice the number of sisters excluding Amisha.

### Step 4: Set Up the Equations
From the statements, we have two equations:
1. \( S = 2(B - 1) \)
2. \( B = 2(S - 1) \)

### Step 5: Substitute and Solve
We can substitute the expression for \( S \) from the first equation into the second equation.

From equation 1:
\[ S = 2(B - 1) \]
Substituting into equation 2:
\[ B = 2(2(B - 1) - 1) \]
This simplifies to:
\[ B = 2(2B - 2 - 1) \]
\[ B = 2(2B - 3) \]
\[ B = 4B - 6 \]
Now, rearranging gives:
\[ 4B - B = 6 \]
\[ 3B = 6 \]
\[ B = 2 \]

### Step 6: Find the Number of Sisters
Now that we have \( B = 2 \), we can substitute back to find \( S \):
Using equation 1:
\[ S = 2(B - 1) \]
\[ S = 2(2 - 1) \]
\[ S = 2(1) \]
\[ S = 2 \]

### Step 7: Total Number of Children
Now we can find the total number of children in the family:
Total = Number of Brothers + Number of Sisters
Total = \( B + S = 2 + 2 = 4 \)

### Final Answer
There are 2 brothers and 2 sisters in the family, making a total of 4 children.

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