The ratio of the prices of two houses A and B was 4 : 5 last year. This year, the price of A is increased by `25%` and that of B by ' 50000. If their prices are now in the ratio 9 : 10, the price of A last year was :

Options

A. `'3,60,000`
B. `'4,50,000`
C. `'4,80,000`
D. `'5,00,000`

Answer

To solve the problem step by step, let's denote the price of house A last year as \(4x\) and the price of house B last year as \(5x\), based on the given ratio of 4:5.

### Step 1: Determine the prices last year
Let:
- Price of house A last year = \(4x\)
- Price of house B last year = \(5x\)

### Step 2: Calculate the new price of house A
This year, the price of house A is increased by 25%. Therefore, the new price of house A will be:
\[ \text{New Price of A} = 4x + 0.25 \times 4x = 4x + x = 5x \]

### Step 3: Calculate the new price of house B
The price of house B is increased by ₹50,000. Therefore, the new price of house B will be:
\[ \text{New Price of B} = 5x + 50000 \]

### Step 4: Set up the ratio of the new prices
According to the problem, the new prices of A and B are in the ratio of 9:10. Thus, we can write:
\[ \frac{5x}{5x + 50000} = \frac{9}{10} \]

### Step 5: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 10 \times 5x = 9 \times (5x + 50000) \]
This simplifies to:
\[ 50x = 45x + 450000 \]

### Step 6: Solve for \(x\)
Now, we can isolate \(x\):
\[ 50x - 45x = 450000 \]
\[ 5x = 450000 \]
\[ x = \frac{450000}{5} = 90000 \]

### Step 7: Calculate the price of house A last year
Now that we have \(x\), we can find the price of house A last year:
\[ \text{Price of A last year} = 4x = 4 \times 90000 = 360000 \]

### Final Answer
The price of house A last year was ₹360,000.

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