The problem provides a frequency distribution of the number of 'dambala miti' (bundles of dambala) supplied to the market daily by three farmers during a month. Each bundle weighs 250g. We are asked to find the approximate mean number of bundles supplied daily, round it to the nearest whole number. Then, given that one bundle sells for Rs. 30, and the market operates for 300 days a year, we need to calculate the annual income of one farmer.

1. Problem Description

The problem provides a frequency distribution of the number of 'dambala miti' (bundles of dambala) supplied to the market daily by three farmers during a month. Each bundle weighs 250g. We are asked to find the approximate mean number of bundles supplied daily, round it to the nearest whole number. Then, given that one bundle sells for Rs. 30, and the market operates for 300 days a year, we need to calculate the annual income of one farmer.

2. Solution Steps

First, we need to calculate the mean number of 'dambala miti' supplied daily. To do this, we will find the midpoint of each class interval, multiply it by the corresponding frequency, sum these products, and then divide by the total frequency.

Class Intervals and Frequencies:

30-32: 1

33-35: 2

36-38: 5

39-41: 10

42-44: 8

45-47: 3

48-50: 1

Midpoints:

(30+32)/2 = 31

(33+35)/2 = 34

(36+38)/2 = 37

(39+41)/2 = 40

(42+44)/2 = 43

(45+47)/2 = 46

(48+50)/2 = 49

Now, we calculate the sum of (midpoint * frequency):

$(31 * 1) + (34 * 2) + (37 * 5) + (40 * 10) + (43 * 8) + (46 * 3) + (49 * 1) = 31 + 68 + 185 + 400 + 344 + 138 + 49 = 1215$

The total frequency is:

$1 + 2 + 5 + 10 + 8 + 3 + 1 = 30$

The mean number of bundles supplied daily is:

$\frac{1215}{30} = 40.5$

Rounding to the nearest whole number, we get 41 bundles per day.

Since the problem states that there are three farmers, the 41 bundles represent the total number of bundles supplied by all three. Therefore, the average bundles supplied by each farmer is $\frac{41}{3}$.

Since the question asks for the income of 'one' farmer, it is implying the data is already representative of 'one' farmer. Hence, we continue with 41 bundles.

Each bundle sells for Rs.

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The total income for the three farmers for 300 days is:

$41 \text{ bundles/day} * 30 \text{ Rs/bundle} * 300 \text{ days} = 369000 \text{ Rs}$

Now, we need to divide by 3 to get the income of one farmer.

Income of one farmer = $369000 / 3 = 123000$

The average number of bundles supplied by each farmer would be $40.5/3 \approx 13.5$. Rounding to nearest whole number, approximately

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Income of one farmer would be $14 \text{ bundles/day} * 30 \text{ Rs/bundle} * 300 \text{ days} = 126000 \text{ Rs}$

However, the problem implies that we already computed the bundles supplied *per farmer* in the initial table given. So, we should use the derived average of 40.5 bundles, round to 41, and find the earnings PER FARMER.

Income of *three* farmers = 41 * 30 * 300 = 369000

Income of *one* farmer = 369000/3 = 123000

3. Final Answer

The annual income of one farmer is Rs. 123,

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