The ratio of the prices of two fans was `16: 23`. Two years later, when the price of the first fan had risen by 10% and that of the second by Rs 477, the ratio of their prices became `11: 20`. Find the original prices of the two fans.

Answer

To find the original prices of the two fans, we can follow these steps:

### Step 1: Set up the initial prices based on the given ratio
Let the original prices of the two fans be represented as:
- Price of Fan 1 = 16x
- Price of Fan 2 = 23x

### Step 2: Calculate the prices after 2 years
After 2 years:
- The price of Fan 1 increases by 10%. Therefore, the new price of Fan 1 becomes:
\[ \text{New Price of Fan 1} = 16x + 0.1 \times 16x = 16x \times 1.1 = 17.6x \]

- The price of Fan 2 increases by Rs 477. Therefore, the new price of Fan 2 becomes:
\[ \text{New Price of Fan 2} = 23x + 477 \]

### Step 3: Set up the equation based on the new ratio
According to the problem, after 2 years, the ratio of the prices of the two fans becomes 11:20. We can write this as:
\[ \frac{17.6x}{23x + 477} = \frac{11}{20} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 20 \times 17.6x = 11 \times (23x + 477) \]

### Step 5: Simplify the equation
Expanding both sides:
\[ 352x = 253x + 5247 \]

### Step 6: Solve for x
Now, rearranging the equation:
\[ 352x - 253x = 5247 \]
\[ 99x = 5247 \]
\[ x = \frac{5247}{99} = 53 \]

### Step 7: Find the original prices of the fans
Now that we have the value of x, we can find the original prices:
- Price of Fan 1:
\[ 16x = 16 \times 53 = 848 \]

- Price of Fan 2:
\[ 23x = 23 \times 53 = 1219 \]

### Final Answer
The original prices of the two fans are:
- Price of Fan 1 = Rs 848
- Price of Fan 2 = Rs 1219

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