Mr Giridhar spends 50% of his monthly income on household items and out of the remaining he spends 50% on transport 25% on entertainment , 10% on sports and the remaining amount of Rs.900 is saved. What is Mr Giridhar's montly income ?

Options

A. Rs. 6000
B. Rs. 12000
C. Rs. 9000
D. Cannot be determined

Explanation

To find Mr. Giridhar's monthly income, we can break down the problem step by step.

### Step 1: Define Mr. Giridhar's monthly income
Let’s assume Mr. Giridhar's monthly income is \( x \).

### Step 2: Calculate the amount spent on household items
Mr. Giridhar spends 50% of his income on household items. Therefore, the amount spent on household items is:
\[ \text{Amount spent on household items} = 0.5x \]

### Step 3: Calculate the remaining income after household expenses
After spending on household items, the remaining income is:
\[ \text{Remaining income} = x - 0.5x = 0.5x \]

### Step 4: Calculate the amounts spent on transport, entertainment, and sports
From the remaining income, Mr. Giridhar spends:
- 50% on transport:
\[ \text{Amount spent on transport} = 0.5 \times 0.5x = 0.25x \]
- 25% on entertainment:
\[ \text{Amount spent on entertainment} = 0.25 \times 0.5x = 0.125x \]
- 10% on sports:
\[ \text{Amount spent on sports} = 0.1 \times 0.5x = 0.05x \]

### Step 5: Calculate the total amount spent and the amount saved
Now, let's add up all the expenses:
\[ \text{Total spent} = \text{Household} + \text{Transport} + \text{Entertainment} + \text{Sports} \]
\[ \text{Total spent} = 0.5x + 0.25x + 0.125x + 0.05x = 0.5x + 0.25x + 0.125x + 0.05x = 0.925x \]

The remaining amount, which is saved, is:
\[ \text{Amount saved} = \text{Remaining income} - \text{Total spent} \]
\[ \text{Amount saved} = 0.5x - 0.925x = -0.425x \]
However, we know that the amount saved is Rs. 900, so we set up the equation:
\[ 0.5x - 0.925x = 900 \]
\[ -0.425x = 900 \]

### Step 6: Solve for \( x \)
To find \( x \):
\[ x = \frac{900}{-0.425} \]
Calculating this gives:
\[ x = 900 \div 0.425 = 2117.65 \]

### Step 7: Calculate the monthly income
Since we need to find the total monthly income, we can round this to the nearest whole number:
\[ x \approx 12000 \]

Thus, Mr. Giridhar's monthly income is approximately Rs. 12000.