The ratio of personal income of A and B of last year is 12:25. The ratio of last year's income and current year's income of A and B is 4:7 and 5 : 2 respectively. The sum of current income of both is Rs. 31000. Then find out A and B's current income separately.

Options

A. `21000,10000`
B. `25000,7000`
C. `20000,11000`
D. `19000,12000`

Answer

To solve the problem step by step, we will use the given ratios and the total current income of A and B.

### Step 1: Define the last year incomes of A and B
Let the last year income of A be \( 12x \) and the last year income of B be \( 25x \), based on the ratio of their incomes which is given as 12:25.

### Step 2: Define the current incomes of A and B
According to the problem, the ratio of last year's income to current year's income for A is 4:7. Therefore, we can express A's current income as:
\[ \text{Current Income of A} = \frac{7}{4} \times \text{Last Year Income of A} = \frac{7}{4} \times 12x = 21x \]

Similarly, for B, the ratio of last year's income to current year's income is 5:2. Thus, we can express B's current income as:
\[ \text{Current Income of B} = \frac{2}{5} \times \text{Last Year Income of B} = \frac{2}{5} \times 25x = 10x \]

### Step 3: Set up the equation for the total current income
We know that the sum of the current incomes of A and B is Rs. 31,000. Therefore, we can write:
\[ 21x + 10x = 31000 \]

### Step 4: Solve for \( x \)
Combining the terms gives:
\[ 31x = 31000 \]
Now, divide both sides by 31:
\[ x = \frac{31000}{31} = 1000 \]

### Step 5: Calculate the current incomes of A and B
Now that we have the value of \( x \), we can find the current incomes:
- Current Income of A:
\[ 21x = 21 \times 1000 = 21000 \]
- Current Income of B:
\[ 10x = 10 \times 1000 = 10000 \]

### Final Answer
Thus, the current incomes of A and B are:
- A's current income = Rs. 21,000
- B's current income = Rs. 10,000

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