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 remaining amount of Rs. 900 is saved. What is Mr. Giridhar's monthly income?

Options

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

Answer

To find Mr. Giridhar's monthly income, we can follow these steps:

### Step 1: Define the Monthly Income
Let Mr. Giridhar's monthly income be \( x \) rupees.

### 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:
\[ \text{Amount spent on household items} = \frac{50}{100} \times x = 0.5x \]

### Step 3: Calculate the Remaining Amount After Household Expenses
After spending on household items, the remaining amount is:
\[ \text{Remaining amount} = x - 0.5x = 0.5x \]

### Step 4: Calculate the Amount Spent on Other Expenses
Out of the remaining amount, Mr. Giridhar spends:
- 50% on transport
- 25% on entertainment
- 10% on sports

Total percentage spent on transport, entertainment, and sports is:
\[ 50\% + 25\% + 10\% = 85\% \]
Thus, the amount spent on these three categories is:
\[ \text{Amount spent on transport, entertainment, and sports} = \frac{85}{100} \times 0.5x = 0.425x \]

### Step 5: Calculate the Remaining Amount After All Expenses
The remaining amount after all expenses is:
\[ \text{Remaining amount} = 0.5x - 0.425x = 0.075x \]

### Step 6: Set Up the Equation with the Saved Amount
According to the problem, the remaining amount is Rs. 900. Therefore, we can set up the equation:
\[ 0.075x = 900 \]

### Step 7: Solve for \( x \)
To find \( x \), we divide both sides by 0.075:
\[ x = \frac{900}{0.075} \]
Calculating the right-hand side:
\[ x = 12000 \]

### Conclusion
Mr. Giridhar's monthly income is Rs. 12,000.

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