Sima has rsX, `60%` of which she keeps aside for a Vacation .and the remaining she distributes amongst her brothers (A and B) in the ratio .of `2 :3`. If the difference between the amount received by A and the amount Sima kept aside for vacation was rs17600, what is the value of X (in rs)?

Options

A. 40000
B. 60000
C. 42000
D. 80000

Answer

To solve the problem step by step, we will break down the information given and use algebra to find the value of X.

### Step 1: Understand the problem
Sima has a total amount of Rs. X. She keeps aside 60% of this amount for a vacation and distributes the remaining 40% among her brothers A and B in the ratio of 2:3.

### Step 2: Calculate the amount kept for vacation
The amount Sima keeps aside for vacation is:
\[ \text{Vacation Amount} = 0.6X \]

### Step 3: Calculate the remaining amount
The remaining amount after keeping aside for vacation is:
\[ \text{Remaining Amount} = X - 0.6X = 0.4X \]

### Step 4: Distribute the remaining amount
Let the amounts received by A and B be \(2Y\) and \(3Y\) respectively, where \(Y\) is a common factor. According to the ratio:
\[ 2Y + 3Y = 0.4X \]
\[ 5Y = 0.4X \]
From this, we can express \(Y\) in terms of \(X\):
\[ Y = \frac{0.4X}{5} = \frac{0.08X}{1} \]

### Step 5: Calculate the amounts received by A and B
The amount received by A is:
\[ A = 2Y = 2 \times \frac{0.08X}{1} = 0.16X \]
The amount received by B is:
\[ B = 3Y = 3 \times \frac{0.08X}{1} = 0.24X \]

### Step 6: Set up the equation based on the given difference
According to the problem, the difference between the amount received by A and the amount Sima kept aside for vacation is Rs. 17600:
\[ A - \text{Vacation Amount} = 17600 \]
Substituting the values we have:
\[ 0.16X - 0.6X = 17600 \]
\[ -0.44X = 17600 \]

### Step 7: Solve for X
To find \(X\), we multiply both sides by -1:
\[ 0.44X = -17600 \]
Now, divide both sides by 0.44:
\[ X = \frac{17600}{0.44} \]
Calculating this gives:
\[ X = 40000 \]

### Final Answer
The value of \(X\) is Rs. 40000.

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