Manoj gave `60%` of his salary to his wife invested rest amount in mutual funds. His wife spends `30%` amount on grocery and `20%` on rent. From remaining amount, she purchased gold worth Rs. 18000. Find salry of Manoj.

Options

A. Rs 60000
B. Rs 54000
C. Rs 64000
D. Rs 58000

Answer

To find Manoj's salary, we can follow these steps:

### Step 1: Define the variables
Let Manoj's salary be \( x \).

### Step 2: Calculate the amount given to his wife
Manoj gives 60% of his salary to his wife. Therefore, the amount given to his wife is:
\[ \text{Amount given to wife} = 60\% \text{ of } x = \frac{60}{100} \times x = 0.6x \]

### Step 3: Calculate the amount spent by his wife
His wife spends 30% of the amount she received on groceries and 20% on rent. We can calculate these amounts as follows:
- Amount spent on groceries:
\[ \text{Grocery} = 30\% \text{ of } 0.6x = \frac{30}{100} \times 0.6x = 0.18x \]
- Amount spent on rent:
\[ \text{Rent} = 20\% \text{ of } 0.6x = \frac{20}{100} \times 0.6x = 0.12x \]

### Step 4: Calculate the total amount spent
Now, we can find the total amount spent by his wife on groceries and rent:
\[ \text{Total spent} = \text{Grocery} + \text{Rent} = 0.18x + 0.12x = 0.30x \]

### Step 5: Calculate the remaining amount
The remaining amount after spending on groceries and rent is:
\[ \text{Remaining amount} = \text{Amount given to wife} - \text{Total spent} = 0.6x - 0.30x = 0.30x \]

### Step 6: Set up the equation for the gold purchase
From the remaining amount, his wife purchased gold worth Rs. 18,000. Therefore, we can set up the equation:
\[ 0.30x = 18,000 \]

### Step 7: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = \frac{18,000}{0.30} \]
Calculating this gives:
\[ x = 18,000 \times \frac{100}{30} = 18,000 \times \frac{10}{3} = 60,000 \]

### Conclusion
Thus, Manoj's salary is:
\[ \text{Salary of Manoj} = Rs. 60,000 \]

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