The incomes of X and Y are in the ratio `5:6` and their expendi-tures are in the ratio `6 : 5`. If X saves Rs. 7000 and Y saves Rs. 15000. what will be the income (in Rs.) of X?

Options

A. 28000
B. 20000
C. 25000
D. 24000

Answer

To find the income of X, we will follow these steps:

### Step 1: Define the Incomes and Expenditures
Let the incomes of X and Y be represented as:
- Income of X = 5x
- Income of Y = 6x

Let the expenditures of X and Y be represented as:
- Expenditure of X = 6y
- Expenditure of Y = 5y

### Step 2: Express Expenditures in Terms of Savings
We know that:
- Savings of X = Income of X - Expenditure of X
- Savings of Y = Income of Y - Expenditure of Y

From the problem, we have:
- Savings of X = Rs. 7000
- Savings of Y = Rs. 15000

Thus, we can write:
1. \( 5x - 6y = 7000 \) (1)
2. \( 6x - 5y = 15000 \) (2)

### Step 3: Solve the System of Equations
We will solve equations (1) and (2) simultaneously.

From equation (1):
\[ 5x - 6y = 7000 \]
Rearranging gives us:
\[ 5x = 6y + 7000 \]
\[ x = \frac{6y + 7000}{5} \] (3)

Now substitute equation (3) into equation (2):
\[ 6\left(\frac{6y + 7000}{5}\right) - 5y = 15000 \]

Multiply through by 5 to eliminate the fraction:
\[ 6(6y + 7000) - 25y = 75000 \]
\[ 36y + 42000 - 25y = 75000 \]
\[ 11y + 42000 = 75000 \]
\[ 11y = 75000 - 42000 \]
\[ 11y = 33000 \]
\[ y = 3000 \]

### Step 4: Find the Value of x
Now substitute the value of y back into equation (3) to find x:
\[ x = \frac{6(3000) + 7000}{5} \]
\[ x = \frac{18000 + 7000}{5} \]
\[ x = \frac{25000}{5} \]
\[ x = 5000 \]

### Step 5: Calculate the Income of X
Now we can find the income of X:
\[ \text{Income of X} = 5x = 5(5000) = 25000 \]

### Final Answer
The income of X is Rs. 25000.

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