Shivam spent `20%` & `32%` of his total monthly salary on children's education & food respectively. He spent `((5)/(8))^(th)` of his remaining monthly salary on medical facilites. If difference between amount spent by him on medical facilities and food is Rs.1080, then find amount spent by Shivam on children's education.

Options

A. Rs. 15000
B. Rs.10800
C. Rs.16200
D. Rs.21000

Answer

To solve the problem step by step, we will follow the information given in the question.

### Step 1: Define the total monthly salary
Let Shivam's total monthly salary be \( 100X \).

### Step 2: Calculate the amount spent on children's education
Shivam spends \( 20\% \) of his total salary on children's education:
\[ \text{Amount spent on children's education} = 20\% \text{ of } 100X = \frac{20}{100} \times 100X = 20X \]

### Step 3: Calculate the amount spent on food
Shivam spends \( 32\% \) of his total salary on food:
\[ \text{Amount spent on food} = 32\% \text{ of } 100X = \frac{32}{100} \times 100X = 32X \]

### Step 4: Calculate the remaining salary after education and food expenses
Total amount spent on children's education and food:
\[ \text{Total spent} = 20X + 32X = 52X \]
Remaining salary:
\[ \text{Remaining salary} = 100X - 52X = 48X \]

### Step 5: Calculate the amount spent on medical facilities
Shivam spends \( \frac{5}{8} \) of his remaining salary on medical facilities:
\[ \text{Amount spent on medical facilities} = \frac{5}{8} \times 48X = 30X \]

### Step 6: Set up the equation based on the difference between food and medical expenses
According to the problem, the difference between the amount spent on medical facilities and food is Rs. 1080:
\[ \text{Difference} = \text{Amount spent on food} - \text{Amount spent on medical facilities} \]
Substituting the values:
\[ 32X - 30X = 1080 \]
This simplifies to:
\[ 2X = 1080 \]

### Step 7: Solve for \( X \)
\[ X = \frac{1080}{2} = 540 \]

### Step 8: Calculate the amount spent on children's education
Now, we can find the amount spent on children's education:
\[ \text{Amount spent on children's education} = 20X = 20 \times 540 = 10800 \]

### Final Answer
The amount spent by Shivam on children's education is Rs. 10,800.

---