Understanding Family Expenditure and Data Interpretation

This question requires us to analyze the provided table showing the percentage distribution of a family's expenditure across different categories (budget heads) for two years, 2020 and 2021. We are also given the total income for each of these years. The specific task is to find the ratio of the amount spent on 'Travel' in 2020 compared to the amount spent on 'Travel' in 2021.

Analyzing the Provided Data Table

Let's first look at the data provided in the table:

We are also given the total income for each year:

• Total Income in 2020: Rs. 50000
• Total Income in 2021: Rs. 75000

Calculating Travel Expenditure for Each Year

To find the ratio of the amount spent on Travel, we first need to calculate the actual amount spent on Travel in each year. The amount spent on any budget head is the percentage of expenditure for that head multiplied by the total income for that year.

Travel Expenditure in 2020

From the table, the percentage expenditure on Travel in 2020 was 34%. The total income in 2020 was Rs. 50000.

Amount spent on Travel in 2020 = 34% of Rs. 50000

Using mathematical expression:

\(\text{Amount (2020)} = \frac{34}{100} \times 50000\)

\(\text{Amount (2020)} = 34 \times 500\)

\(\text{Amount (2020)} = 17000\)

So, the family spent Rs. 17000 on Travel in 2020.

Travel Expenditure in 2021

From the table, the percentage expenditure on Travel in 2021 was 24%. The total income in 2021 was Rs. 75000.

Amount spent on Travel in 2021 = 24% of Rs. 75000

Using mathematical expression:

\(\text{Amount (2021)} = \frac{24}{100} \times 75000\)

\(\text{Amount (2021)} = 24 \times 750\)

\(\text{Amount (2021)} = 18000\)

So, the family spent Rs. 18000 on Travel in 2021.

Determining the Ratio of Travel Expenditure

Now that we have the amount spent on Travel in both years, we can find the ratio of the total amount spent on Travel by the family in 2020 to that in 2021.

Ratio = Amount spent on Travel in 2020 : Amount spent on Travel in 2021

Ratio = 17000 : 18000

To simplify the ratio, we can divide both sides by the greatest common divisor. We can see that both numbers end in three zeros, so we can divide by 1000.

Ratio = \(\frac{17000}{1000} : \frac{18000}{1000}\)

Ratio = 17 : 18

This ratio 17:18 cannot be simplified further as 17 and 18 have no common factors other than 1.

Conclusion

The ratio of the total amount spent on Travel by the family in 2020 to that in 2021 is 17 ∶ 18.

Revision Table: Key Concepts

Additional Information: Data Interpretation Tips

• Read the Question Carefully: Understand exactly what is being asked (e.g., ratio of which quantities, for which years).
• Identify Relevant Data: Focus only on the rows/columns in the table and the additional information (like total income) that are needed for the calculation.
• Perform Calculations Step-by-Step: Break down the problem into smaller parts (e.g., calculate expenditure for Year 1, calculate expenditure for Year 2, then calculate the ratio).
• Pay Attention to Units: Ensure consistency (e.g., working with amounts in Rupees after calculating from percentages).
• Simplify Ratios/Fractions: Always present the final ratio or fraction in its simplest form unless otherwise specified.
• Check Your Work: Quickly review your calculations to avoid errors.