Two times of A's salary is five times of B's salary and four times of B's salary is twice C’s salary. What is A's salary if C’s salary is Rs.1,600?

Options

A. Rs.2,000
B. Rs.2,500
C. Rs.2,600
D. Rs.3,000

Answer

To solve the problem step by step, let's denote the salaries of A, B, and C as follows:

- Let A's salary = A
- Let B's salary = B
- Let C's salary = C

Given:
1. Two times A's salary is equal to five times B's salary.
\[ 2A = 5B \quad \text{(Equation 1)} \]

2. Four times B's salary is equal to twice C's salary.
\[ 4B = 2C \quad \text{(Equation 2)} \]

We also know that C's salary is Rs. 1,600:
\[ C = 1600 \]

### Step 1: Solve for B using Equation 2

From Equation 2, we can express B in terms of C:
\[ 4B = 2C \implies B = \frac{2C}{4} = \frac{C}{2} \]
Substituting the value of C:
\[ B = \frac{1600}{2} = 800 \]

### Step 2: Solve for A using Equation 1

Now, substitute B into Equation 1 to find A:
\[ 2A = 5B \implies A = \frac{5B}{2} \]
Substituting the value of B:
\[ A = \frac{5 \times 800}{2} = \frac{4000}{2} = 2000 \]

### Conclusion

Thus, A's salary is Rs. 2,000.