Amit earns Rs.` 32000` per month. He spends `(1)/(4)` of his income on food, `(3)/(10)` of the remainder on house rent and `(5)/(21)` of the remainder on the education of children. How much money is still left with him?

Options

A. Rs. `12600`
B. Rs. `12500`
C. Rs. `12700`
D. Rs. `12800`

Answer

To find out how much money Amit has left after his expenditures, we will follow these steps:

1. **Calculate the amount spent on food:**
Amit spends \( \frac{1}{4} \) of his income on food.
\[ \text{Amount spent on food} = \frac{1}{4} \times 32000 = 8000 \]

2. **Calculate the remainder after food expenses:**
\[ \text{Remainder after food} = 32000 - 8000 = 24000 \]

3. **Calculate the amount spent on house rent:**
Amit spends \( \frac{3}{10} \) of the remainder on house rent.
\[ \text{Amount spent on house rent} = \frac{3}{10} \times 24000 = 7200 \]

4. **Calculate the remainder after house rent expenses:**
\[ \text{Remainder after house rent} = 24000 - 7200 = 16800 \]

5. **Calculate the amount spent on children's education:**
Amit spends \( \frac{5}{21} \) of the remainder on children's education.
\[ \text{Amount spent on education} = \frac{5}{21} \times 16800 = 4000 \]

6. **Calculate the final amount left:**
\[ \text{Final amount left} = 16800 - 4000 = 12800 \]

Thus, the amount of money Amit has left after all his expenditures is **Rs. 12,800**.