A person earns ₹ 54000 per month. He spends `2/15` of his earnings on house rent, `4/9` of his earnings on other household items and saves and remaining. What fraction of amount is the savings in his earnings ?

Options

A. `19/45`
B. `17/45`
C. `13/24`
D. `11/25`

Explanation

To find the fraction of the amount saved from the earnings, we will follow these steps:

### Step 1: Calculate the amount spent on house rent
The person spends \( \frac{2}{15} \) of his earnings on house rent.

- Total earnings = ₹ 54,000
- Amount spent on house rent = \( \frac{2}{15} \times 54,000 \)

**Calculation:**
\[ \text{Amount spent on house rent} = \frac{2}{15} \times 54,000 = \frac{108,000}{15} = 7,200 \]

### Step 2: Calculate the amount spent on other household items
The person spends \( \frac{4}{9} \) of his earnings on other household items.

- Amount spent on other household items = \( \frac{4}{9} \times 54,000 \)

**Calculation:**
\[ \text{Amount spent on other household items} = \frac{4}{9} \times 54,000 = \frac{216,000}{9} = 24,000 \]

### Step 3: Calculate total expenditure
Now, we will sum the amounts spent on house rent and other household items.

**Calculation:**
\[ \text{Total expenditure} = \text{Amount spent on house rent} + \text{Amount spent on other household items} \]
\[ \text{Total expenditure} = 7,200 + 24,000 = 31,200 \]

### Step 4: Calculate the savings
To find the savings, we subtract the total expenditure from the total earnings.

**Calculation:**
\[ \text{Savings} = \text{Total earnings} - \text{Total expenditure} \]
\[ \text{Savings} = 54,000 - 31,200 = 22,800 \]

### Step 5: Calculate the fraction of savings in his earnings
Finally, we will find the fraction of the savings in relation to his total earnings.

**Calculation:**
\[ \text{Fraction of savings} = \frac{\text{Savings}}{\text{Total earnings}} = \frac{22,800}{54,000} \]

To simplify this fraction, we can divide both the numerator and the denominator by 22,800.

\[ \text{Fraction of savings} = \frac{22,800 \div 22,800}{54,000 \div 22,800} = \frac{1}{2.368421} \]

This fraction can be further simplified to approximately \( \frac{5}{12} \).

### Final Answer
The fraction of the amount that is the savings in his earnings is \( \frac{5}{12} \).

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