When the fare of a certain journey by an airliner was increased in the ratio `5 : 7` the cost of the ticket for the journey became Rs. 1.421. Find the increase in the fare.

Answer

To solve the problem step by step, we will follow the given information and derive the original fare and the increase in fare.

### Step 1: Define the original fare
Let the original fare be denoted as \( x \).

### Step 2: Define the new fare based on the ratio
According to the problem, the fare was increased in the ratio \( 5:7 \). This means:
\[ \frac{x}{5} = \frac{y}{7} \]
where \( y \) is the new fare. From this, we can express \( y \) in terms of \( x \):
\[ y = \frac{7}{5} x \]

### Step 3: Set up the equation with the new fare
We are given that the new fare \( y \) is Rs. 1421. Therefore, we can set up the equation:
\[ \frac{7}{5} x = 1421 \]

### Step 4: Solve for the original fare \( x \)
To find \( x \), we can rearrange the equation:
\[ x = 1421 \times \frac{5}{7} \]
Calculating this gives:
\[ x = 1421 \times \frac{5}{7} = 1421 \times 0.7142857 \approx 1015 \]

### Step 5: Calculate the increase in fare
Now that we have the original fare \( x \) as Rs. 1015, we can find the increase in fare by subtracting the original fare from the new fare:
\[ \text{Increase in fare} = y - x = 1421 - 1015 \]
Calculating this gives:
\[ \text{Increase in fare} = 406 \]

### Final Answer
Thus, the increase in the fare is Rs. 406.

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