A spend `30%` of his monthly salary on house rent, `40%` of the remainings salary on clothing and he distributes his remaining monthly salary among his two daughters and a son in the ration `5 : 5 : 4`. If difference of A's monthly expenditure on Clothing and monthly amount given by A to his son is Rs. 24000, then find A's annual expenditure on house rent.

Options

A. 500000
B. 540000
C. 550000
D. 560000

Answer

To solve the problem step by step, let's denote A's monthly salary as \( S \).

### Step 1: Calculate the amount spent on house rent
A spends 30% of his monthly salary on house rent.
\[ \text{House Rent} = 0.30 \times S = 0.3S \]

### Step 2: Calculate the remaining salary after house rent
The remaining salary after paying for house rent is:
\[ \text{Remaining Salary} = S - 0.3S = 0.7S \]

### Step 3: Calculate the amount spent on clothing
A spends 40% of the remaining salary on clothing.
\[ \text{Clothing Expenditure} = 0.40 \times \text{Remaining Salary} = 0.40 \times 0.7S = 0.28S \]

### Step 4: Calculate the remaining salary after clothing
The remaining salary after paying for clothing is:
\[ \text{Remaining Salary after Clothing} = 0.7S - 0.28S = 0.42S \]

### Step 5: Distributing the remaining salary among children
A distributes the remaining salary among his two daughters and a son in the ratio \( 5:5:4 \).
The total parts in the ratio = \( 5 + 5 + 4 = 14 \).

The amount given to each child:
- Each daughter receives:
\[ \text{Amount to each daughter} = \frac{5}{14} \times 0.42S \]
- The son receives:
\[ \text{Amount to son} = \frac{4}{14} \times 0.42S = \frac{2}{7} \times 0.42S \]

### Step 6: Calculate the amount given to the son
\[ \text{Amount to son} = \frac{2 \times 0.42S}{7} = \frac{0.84S}{7} = 0.12S \]

### Step 7: Set up the equation based on the difference given
According to the problem, the difference between A's monthly expenditure on clothing and the amount given to his son is Rs. 24000.
\[ \text{Clothing Expenditure} - \text{Amount to Son} = 24000 \]
Substituting the values:
\[ 0.28S - 0.12S = 24000 \]
\[ 0.16S = 24000 \]

### Step 8: Solve for S
\[ S = \frac{24000}{0.16} = 150000 \]

### Step 9: Calculate A's annual expenditure on house rent
Now, we can calculate the monthly expenditure on house rent:
\[ \text{House Rent} = 0.3S = 0.3 \times 150000 = 45000 \]
To find the annual expenditure on house rent:
\[ \text{Annual House Rent} = 45000 \times 12 = 540000 \]

### Final Answer
A's annual expenditure on house rent is Rs. 540000.

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