Ram and Shyam both save `30%` and `44%` of their monthly incomes respectively. The amount they spent each month is equal. The difference between monthly incomes of Ram and Shyam is ₹5000. What is Ram’s monthly income ?

Options

A. ₹ 20000
B. cannot be determined
C. ₹ 30000
D. ₹ 36000

Answer

To find Ram's monthly income, we can follow these steps:

### Step 1: Define the variables
Let Ram's monthly income be \( R \) and Shyam's monthly income be \( S \).

### Step 2: Set up the equations based on the information given
1. Ram saves 30% of his income, so his expenditure is:
\[ \text{Expenditure of Ram} = R - 0.30R = 0.70R \]
2. Shyam saves 44% of his income, so his expenditure is:
\[ \text{Expenditure of Shyam} = S - 0.44S = 0.56S \]
3. Since their expenditures are equal:
\[ 0.70R = 0.56S \]

### Step 3: Use the difference in their incomes
We know that the difference between their incomes is ₹5000:
\[ R - S = 5000 \quad \text{(1)} \]

### Step 4: Rearranging the expenditure equation
From the equation \( 0.70R = 0.56S \), we can express \( S \) in terms of \( R \):
\[ S = \frac{0.70R}{0.56} = \frac{70R}{56} = \frac{5R}{4} \quad \text{(2)} \]

### Step 5: Substitute equation (2) into equation (1)
Substituting \( S \) from equation (2) into equation (1):
\[ R - \frac{5R}{4} = 5000 \]
To simplify:
\[ R - \frac{5R}{4} = \frac{4R}{4} - \frac{5R}{4} = -\frac{R}{4} = 5000 \]
Multiplying both sides by -4:
\[ R = -5000 \times -4 = 20000 \]

### Step 6: Conclusion
Thus, Ram's monthly income is:
\[ \boxed{20000} \]

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