Sameer spends `24%` of his monthly income on food, `15% `on children's education. `25%` of the remaining is spent on entertainment and `20% ` on travelling. If he is left with Rs. 10736. Find his monthly income.

Answer

To find Sameer's monthly income based on his spending habits, we can follow these steps:

### Step 1: Define the Monthly Income
Let Sameer's monthly income be represented as \( x \).

### Step 2: Calculate the Amount Spent on Food and Education
- Sameer spends \( 24\% \) of his income on food:
\[ \text{Amount spent on food} = \frac{24}{100} \times x = 0.24x \]

- Sameer spends \( 15\% \) of his income on children's education:
\[ \text{Amount spent on education} = \frac{15}{100} \times x = 0.15x \]

### Step 3: Calculate the Remaining Income
To find the remaining income after spending on food and education, we subtract these amounts from the total income:
\[ \text{Remaining income} = x - (0.24x + 0.15x) = x - 0.39x = 0.61x \]

### Step 4: Calculate the Amount Spent on Entertainment and Travelling
- Sameer spends \( 25\% \) of the remaining income on entertainment:
\[ \text{Amount spent on entertainment} = \frac{25}{100} \times (0.61x) = 0.25 \times 0.61x = 0.1525x \]

- Sameer spends \( 20\% \) of the remaining income on travelling:
\[ \text{Amount spent on travelling} = \frac{20}{100} \times (0.61x) = 0.20 \times 0.61x = 0.122x \]

### Step 5: Calculate Total Amount Spent on Entertainment and Travelling
Now, we can find the total amount spent on entertainment and travelling:
\[ \text{Total spent on entertainment and travelling} = 0.1525x + 0.122x = 0.2745x \]

### Step 6: Calculate the Final Amount Left
The amount left after all expenditures is given as \( 10,736 \):
\[ \text{Final amount left} = \text{Remaining income} - \text{Total spent on entertainment and travelling} \]
\[ 10,736 = 0.61x - 0.2745x \]
\[ 10,736 = (0.61 - 0.2745)x = 0.3355x \]

### Step 7: Solve for Monthly Income \( x \)
To find \( x \), we rearrange the equation:
\[ x = \frac{10,736}{0.3355} \]
Calculating this gives:
\[ x \approx 32,000 \]

### Conclusion
Sameer's monthly income is approximately \( \text{Rs. } 32,000 \).

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