The ratio of personal income of A and B of last year is 9:12. The ratio of last year's income and current year's income of A and B is 3 : 4 and 4 : 5 respectively. The sum of current income of both is Rs. 54000. Then find out A and B's current income separately

Options

A. `2400,3000`
B. `3000,2600`
C. `24000,30000`
D. `4200,5400`

Answer

To solve the problem step by step, we will follow the given ratios and relationships between the incomes of A and B.

### Step 1: Establish the Ratios
The ratio of last year's income of A and B is given as:
- A : B = 9 : 12

Let last year's income of A = 9x and last year's income of B = 12x.

### Step 2: Current Year Income Ratios
The ratio of last year's income to current year's income for A is given as:
- Last year : Current year = 3 : 4

This means:
- Current year income of A = (4/3) * Last year income of A = (4/3) * 9x = 12x

The ratio of last year's income to current year's income for B is given as:
- Last year : Current year = 4 : 5

This means:
- Current year income of B = (5/4) * Last year income of B = (5/4) * 12x = 15x

### Step 3: Set Up the Equation
We know that the sum of the current incomes of A and B is Rs. 54,000:
- Current income of A + Current income of B = 54000
- 12x + 15x = 54000

### Step 4: Combine Like Terms
Combine the terms:
- 27x = 54000

### Step 5: Solve for x
Now, we solve for x:
- x = 54000 / 27
- x = 2000

### Step 6: Calculate Current Incomes
Now we can find the current incomes of A and B:
- Current income of A = 12x = 12 * 2000 = 24000
- Current income of B = 15x = 15 * 2000 = 30000

### Final Answer
- A's current income = Rs. 24000
- B's current income = Rs. 30000

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