Ash's monthly income is `60%` of Deepak's monthly income, `120%` of Maya's monthly income. What is Maya's monthly income, If Deepak's monthly income is Rs.78000?

Options

A. Rs. 39000
B. Rs. 42000
C. Rs. 36000
D. Cannot be determined

Answer

To solve the problem step by step, we will first establish the relationships between the incomes of Ash, Deepak, and Maya based on the percentages given.

### Step 1: Define the incomes based on the problem statement
Let:
- Deepak's monthly income = \( D \)
- Ash's monthly income = \( A \)
- Maya's monthly income = \( M \)

From the problem, we know:
1. \( A = 0.6D \) (Ash's income is 60% of Deepak's income)
2. \( A = 1.2M \) (Ash's income is 120% of Maya's income)

### Step 2: Substitute Deepak's income
We are given that Deepak's monthly income \( D = 78000 \).

### Step 3: Calculate Ash's income using Deepak's income
Using the first equation:
\[ A = 0.6D = 0.6 \times 78000 \]
\[ A = 46800 \]

### Step 4: Use Ash's income to find Maya's income
Now, using the second equation:
\[ A = 1.2M \]
Substituting the value of \( A \):
\[ 46800 = 1.2M \]

### Step 5: Solve for Maya's income
To find \( M \), we rearrange the equation:
\[ M = \frac{46800}{1.2} \]
\[ M = 39000 \]

### Conclusion
Maya's monthly income is \( \text{Rs. } 39000 \).