Three persons A, B, C whose salaries together amount to Rs 72000 spend 80, 85 and 75 percent of their salaries respectively. If their savings are in the ratio `8:9: 20`, then A's salary is:

Options

A. Rs 20,000
B. Rs 16,000
C. Rs 22,000
D. Rs 18,000

Answer

To find A's salary, we will follow these steps:

1. **Understand the given data**:
- Total salaries of A, B, and C = Rs 72000
- Spending percentages: A spends 80%, B spends 85%, C spends 75%
- Savings ratio of A, B, and C = 8:9:20

2. **Calculate the savings in terms of a variable**:
- Let the savings of A be 8x, B be 9x, and C be 20x.

3. **Determine the spending for each person**:
- Since A spends 80%, it saves 20%. Therefore, if A's salary is S_A, then:
\[ \text{Savings of A} = S_A \times 20\% = 0.2 S_A = 8x \implies S_A = \frac{8x}{0.2} = 40x \]
- For B, spending 85% means saving 15%:
\[ \text{Savings of B} = S_B \times 15\% = 0.15 S_B = 9x \implies S_B = \frac{9x}{0.15} = 60x \]
- For C, spending 75% means saving 25%:
\[ \text{Savings of C} = S_C \times 25\% = 0.25 S_C = 20x \implies S_C = \frac{20x}{0.25} = 80x \]

4. **Set up the equation for total salaries**:
- The total salary equation is:
\[ S_A + S_B + S_C = 72000 \]
- Substituting the values we found:
\[ 40x + 60x + 80x = 72000 \]
- Simplifying this gives:
\[ 180x = 72000 \]

5. **Solve for x**:
- Dividing both sides by 180:
\[ x = \frac{72000}{180} = 400 \]

6. **Calculate A's salary**:
- Now substituting x back to find A's salary:
\[ S_A = 40x = 40 \times 400 = 16000 \]

Thus, A's salary is **Rs 16,000**.