Introduction:
When the cost of tobacco was increased by 50%, a certain Harden smoker claimed that the price hike had increased his cost of living by 5%. In order to understand this claim, we need to analyze the situation and calculate the actual impact of the price increase on his cost of living.

Analysis:
To evaluate the impact of the price increase on the smoker's cost of living, we need to consider the following factors:

1. Cost of Tobacco:
The price of tobacco has increased by 50%. This means that if the smoker used to spend $x on tobacco before the price hike, he now has to spend $1.5x to maintain the same scale of consumption.

2. Scale of Consumption:
The smoker claims to maintain his formal scale of consumption. This implies that he continues to consume tobacco at the same level as before the price increase.

3. Total Living Expenses:
The smoker's cost of living includes various expenses apart from tobacco, such as food, housing, transportation, and other daily necessities. These expenses may or may not be affected by the price increase of tobacco.

Calculation:
To calculate the actual impact of the price increase on the smoker's cost of living, we can use the following formula:

% Change in Cost of Living = (Change in Cost of Tobacco / Total Living Expenses) * 100

Given that the cost of tobacco has increased by 50% and the smoker claims that his cost of living has increased by 5%, we can substitute these values into the formula:

5% = (50% / Total Living Expenses) * 100

Simplifying the equation:

Total Living Expenses = 50% / (5% / 100) = 1000%

Conclusion:
Based on the calculation, the smoker's total living expenses have increased by 1000% due to the 50% increase in the cost of tobacco. This implies that the smoker's claim of a 5% increase in his cost of living is inaccurate. The actual impact of the price hike on his cost of living is much higher. It is important to consider all factors and accurately assess the impact of price changes on one's cost of living to make informed decisions and claims.