The incomes of P, Q and R are in the ratio of `5 : 4 : 3` respectively and their expenses are in the ratio of `6 : 5 : 4` respectively. If P saves Rs. 4000 out of an income of Rs. 10000, what will be the saving (In Rs.) of Q?

Options

A. 3000
B. 4500
C. 2000
D. 2500

Answer

To solve the problem step by step, we will follow the given ratios and the information provided.

### Step 1: Understand the Ratios of Incomes and Expenses
The incomes of P, Q, and R are in the ratio of \(5:4:3\). This means:
- Let the income of P = \(5x\)
- Let the income of Q = \(4x\)
- Let the income of R = \(3x\)

The expenses of P, Q, and R are in the ratio of \(6:5:4\). This means:
- Let the expense of P = \(6y\)
- Let the expense of Q = \(5y\)
- Let the expense of R = \(4y\)

### Step 2: Calculate P's Expenditure
We know that P's income is Rs. 10,000 and P saves Rs. 4,000. Therefore, P's expenditure can be calculated as:
\[ \text{Expenditure of P} = \text{Income of P} - \text{Savings of P} = 10000 - 4000 = 6000 \]

### Step 3: Set Up the Equations
From the information above, we can set up the following equations:
1. \(5x = 10000\) (for P's income)
2. \(6y = 6000\) (for P's expenditure)

### Step 4: Solve for x and y
From the first equation:
\[ x = \frac{10000}{5} = 2000 \]

From the second equation:
\[ y = \frac{6000}{6} = 1000 \]

### Step 5: Find Incomes and Expenses of Q
Now we can find the income and expenses of Q using the values of \(x\) and \(y\):
- Income of Q:
\[ \text{Income of Q} = 4x = 4 \times 2000 = 8000 \]

- Expense of Q:
\[ \text{Expense of Q} = 5y = 5 \times 1000 = 5000 \]

### Step 6: Calculate Q's Savings
Now we can calculate Q's savings:
\[ \text{Savings of Q} = \text{Income of Q} - \text{Expense of Q} = 8000 - 5000 = 3000 \]

### Final Answer
The savings of Q is Rs. 3000.

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