P and Q's expenditures are in proportion to the ratio of their incomes. P's income is ₹ 32000 and his expenditure is ₹ 24000. if Q's expenditure is ₹ 36000, then find the income of Q.

Options

A. ₹ 42000
B. ₹ 39000
C. ₹ 48000
D. ₹ 45000

Explanation

To solve the problem step by step, we will use the given information about P and Q's incomes and expenditures.

### Step 1: Write down the known values.
- P's income = ₹32,000
- P's expenditure = ₹24,000
- Q's expenditure = ₹36,000
- Q's income = ? (This is what we need to find)

### Step 2: Set up the proportion based on the problem statement.
The problem states that P and Q's expenditures are in proportion to their incomes. This can be expressed as:
\[ \frac{P's \, expenditure}{P's \, income} = \frac{Q's \, expenditure}{Q's \, income} \]
Substituting the known values, we have:
\[ \frac{24000}{32000} = \frac{36000}{Q's \, income} \]

### Step 3: Simplify the left side of the equation.
We can simplify \(\frac{24000}{32000}\):
\[ \frac{24000 \div 8000}{32000 \div 8000} = \frac{3}{4} \]
So, we can rewrite the equation as:
\[ \frac{3}{4} = \frac{36000}{Q's \, income} \]

### Step 4: Cross-multiply to solve for Q's income.
Cross-multiplying gives us:
\[ 3 \times Q's \, income = 4 \times 36000 \]
Calculating the right side:
\[ 4 \times 36000 = 144000 \]
So, we have:
\[ 3 \times Q's \, income = 144000 \]

### Step 5: Divide both sides by 3 to find Q's income.
\[ Q's \, income = \frac{144000}{3} = 48000 \]

### Conclusion:
Thus, Q's income is ₹48,000.

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