Calculating Mobile Phone Distribution Percentage Difference

The question asks us to find how much less, in percentage terms, the total mobile phone distribution in Madhya Pradesh (M.P.) is compared to the combined distribution in Assam and Punjab under the CONNECT Scheme.

Understanding the Mobile Phone Distribution Data

We are given a table showing the number of mobile phones distributed in Lakhs across seven states and their percentage distribution among different income groups. The total number of mobile phones distributed is 30 Lakhs. Some values in the table are missing.

Finding the Number of Mobile Phones in Each State

We need the number of mobile phones distributed in M.P., Assam, and Punjab.

• Mobile phones in M.P. = 6.5 Lakhs (Given).
• Mobile phones in Assam = 4.2 Lakhs (Given).
• Mobile phones in Punjab = Missing (Marked as '-').

Calculating the Missing Distribution Value for Punjab

The total distribution across all seven states is 30 Lakhs. We can find the number of phones in Punjab by subtracting the sum of distributions in the other six states from the total distribution.

Number of phones in other states = M.P. + Bihar + U.P. + Haryana + Assam + Kerala

\( = 6.5 + 3.4 + 2.5 + 5.2 + 4.2 + 4.7 \)

\( = 26.5 \) Lakhs

Number of phones in Punjab = Total distribution - Number of phones in other states

\( = 30 - 26.5 \)

\( = 3.5 \) Lakhs

So, the number of mobile phones distributed in Punjab is 3.5 Lakhs.

Calculating Combined Distribution in Assam and Punjab

Now we add the number of phones in Assam and Punjab:

Combined distribution (Assam + Punjab) = Assam distribution + Punjab distribution

\( = 4.2 + 3.5 \)

\( = 7.7 \) Lakhs

Calculating Percentage Less

We want to find out what percentage the M.P. distribution (6.5 Lakhs) is less than the combined Assam and Punjab distribution (7.7 Lakhs).

The formula for percentage less is:

\( \text{Percentage less} = \left( \frac{\text{Larger Value} - \text{Smaller Value}}{\text{Larger Value}} \right) \times 100 \)

In this case, the Larger Value is the combined distribution of Assam and Punjab (7.7 Lakhs), and the Smaller Value is the distribution in M.P. (6.5 Lakhs).

\( \text{Percentage less} = \left( \frac{7.7 - 6.5}{7.7} \right) \times 100 \)

\( = \left( \frac{1.2}{7.7} \right) \times 100 \)

Now, we perform the division and multiplication:

\( \frac{1.2}{7.7} \approx 0.155844 \)

\( 0.155844 \times 100 \approx 15.5844 \)

Rounding to two decimal places, we get 15.58%.

Conclusion on Mobile Phone Distribution Comparison

The total distribution of Mobile phones in M.P. (6.5 Lakhs) is approximately 15.58% less than that of in Assam and Punjab together (7.7 Lakhs).

Comparing this value to the given options, we find that 15.58 matches option 1.

Revision Table: Key Mobile Phone Distribution Figures

Additional Information on Percentage Calculations and Data Interpretation

Understanding how to calculate percentage difference and percentage change is crucial for data interpretation questions. The key is always identifying the base value against which the percentage is calculated.

• Percentage Change: Used when comparing a new value to an old value (increase or decrease). Formula: \( \frac{|\text{New Value} - \text{Old Value}|}{\text{Old Value}} \times 100 \).
• Percentage Difference: Used when comparing two values to find the relative difference. Sometimes calculated relative to the average of the two values, but in questions like this asking "% less than" or "% more than", the base is the value being compared against (the "than" value).
• Missing Data: Often in data interpretation tables, some values are missing. These can usually be calculated using totals or percentages provided elsewhere in the table or question. Always look for relationships between the given numbers.
• Data Tables: Carefully read all headings and labels in a table. Note the units (like 'Lakhs' or '%'). Understand what each row and column represents before starting calculations.

This question involved simple arithmetic and the correct application of the percentage less formula after determining all necessary values from the table.