Ram's monthly income is two-fifth of Shyam's monthly income. Ram's annual income is Rs. 3.6 lakh. What is Shyam's annual income ?

Options

A. Rs. 9 lakh
B. Rs. 7.2 lakh
C. Rs. 6 lakh
D. None of these

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the relationship between Ram's and Shyam's incomes.
We know that Ram's monthly income is two-fifths of Shyam's monthly income. We can express this relationship mathematically:
\[ R = \frac{2}{5} S \]
Where \( R \) is Ram's monthly income and \( S \) is Shyam's monthly income.

### Step 2: Calculate Ram's monthly income.
We are given that Ram's annual income is Rs. 3.6 lakh. To find his monthly income, we divide his annual income by 12 (the number of months in a year):
\[ R = \frac{3.6 \text{ lakh}}{12} \]
\[ R = \frac{3.6 \times 100000}{12} \]
\[ R = 30000 \text{ Rs.} \]

### Step 3: Substitute Ram's monthly income into the relationship.
Now that we have Ram's monthly income, we can substitute it into the equation we established in Step 1:
\[ 30000 = \frac{2}{5} S \]

### Step 4: Solve for Shyam's monthly income.
To find Shyam's monthly income \( S \), we can rearrange the equation:
\[ S = 30000 \times \frac{5}{2} \]
\[ S = 30000 \times 2.5 \]
\[ S = 75000 \text{ Rs.} \]

### Step 5: Calculate Shyam's annual income.
Now that we have Shyam's monthly income, we can find his annual income by multiplying his monthly income by 12:
\[ \text{Annual Income of Shyam} = S \times 12 \]
\[ \text{Annual Income of Shyam} = 75000 \times 12 \]
\[ \text{Annual Income of Shyam} = 900000 \text{ Rs.} \]
\[ \text{Annual Income of Shyam} = 9 \text{ lakh} \]

### Conclusion:
Shyam's annual income is Rs. 9 lakh.