Go through the pie chart/s given below and answer the question that follows.
Question: 1
What is the total profit earned by company G for item I and II together?
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To calculate profit, first find the share of the total production based on the ratio, then calculate the percentage profit based on the units produced.
- The total production cost for both items (I and II) by all seven companies is Rs. 25 crore.
- The percentage production by Company G is \( 12% \), so the value of production by Company G is:
\[
\frac{12}{100} \times 25 \, \text{crore} = 3 \, \text{crore}
\]
- The ratio of production between items I and II for Company G is \( 1:2 \), meaning for every 1 unit of item I, 2 units of item II are produced.
- The total units of production are divided in this ratio, so for every 3 units produced, 1 unit is for item I and 2 units are for item II.
- The total profit earned by Company G from item I and item II is calculated using the given profit percentages:
- Profit for Item I: \( 1 \, \text{unit of production} = \frac{1}{3} \times 30 \, \text{percent of 3 crore} = 1 \, \text{crore} \times 0.30 = 0.3 \, \text{crore} \)
- Profit for Item II: \( 2 \, \text{units of production} = \frac{2}{3} \times 24 \, \text{percent of 3 crore} = 2 \, \text{crore} \times 0.24 = 0.48 \, \text{crore} \)
- Total profit from items I and II for Company G:
\[
\text{Total Profit} = 0.3 + 0.48 = 0.78 \, \text{crore} = 78 \, \text{lakh}
\]
Thus, the correct answer is Rs. 78 lakh.
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Question: 2
What is the total profit earned by company B on production of item I and the profit earned by company A on production of item II?
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To calculate total profit, break down the production ratios for each item and apply the profit percentages to the respective production values.
- Profit earned by company B on production of Item I:
- Company B's ratio of production for Item I and Item II is \( 3:2 \).
- Company B's share of total production is \( 11% \) of Rs. 25 crore:
\[
\frac{11}{100} \times 25 = 2.75 \, \text{crore}
\]
- The share of production for Item I is \( \frac{3}{5} \times 2.75 \, \text{crore} = 1.65 \, \text{crore} \).
- The profit earned by company B from Item I is \( 32% \) of 1.65 crore:
\[
\frac{32}{100} \times 1.65 = 0.528 \, \text{crore} = 52.8 \, \text{lakh}
\]
- Profit earned by company A on production of Item II:
- Company A's ratio of production for Item I and Item II is \( 2:3 \).
- Company A's share of total production is \( 15% \) of Rs. 25 crore:
\[
\frac{15}{100} \times 25 = 3.75 \, \text{crore}
\]
- The share of production for Item II is \( \frac{3}{5} \times 3.75 \, \text{crore} = 2.25 \, \text{crore} \).
- The profit earned by company A from Item II is \( 20% \) of 2.25 crore:
\[
\frac{20}{100} \times 2.25 = 0.45 \, \text{crore} = 45 \, \text{lakh}
\]
- Total profit:
The total profit earned is the sum of profits from both items:
\[
52.8 \, \text{lakh} + 45 \, \text{lakh} = 97.8 \, \text{lakh}
\]
Thus, the correct answer is Rs. 97.8 lakh.
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Question: 3
What is the total cost of the production of item I by companies A and C together (in Rs. crore)?
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When solving for specific item production costs, break down the percentage share for each company and apply the production ratio to calculate the cost for each item.
- The total cost of production (both items together) by all seven companies is Rs. 25 crore.
- Company A's production of Item I:
- Company A's share of total production is \( 15% \) of Rs. 25 crore:
\[
\frac{15}{100} \times 25 = 3.75 \, \text{crore}
\]
- The ratio of production between items I and II for Company A is \( 2:3 \).
- The share of production for Item I is \( \frac{2}{5} \times 3.75 \, \text{crore} = 1.5 \, \text{crore} \).
- Company C's production of Item I:
- Company C's share of total production is \( 22% \) of Rs. 25 crore:
\[
\frac{22}{100} \times 25 = 5.5 \, \text{crore}
\]
- The ratio of production between items I and II for Company C is \( 4:1 \).
- The share of production for Item I is \( \frac{4}{5} \times 5.5 \, \text{crore} = 4.4 \, \text{crore} \).
- Total cost of production for Item I by Companies A and C:
\[
1.5 \, \text{crore} + 4.4 \, \text{crore} = 5.9 \, \text{crore}
\]
Thus, the correct answer is 5.9 crore.
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Question: 4
Cost of production of item I by company F is what percent of the cost of production of item II by company D?
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To calculate percentages, divide the cost of the smaller part by the cost of the larger part and multiply by 100 to get the percentage.
- The total production cost for both items (I and II) by all seven companies is Rs. 25 crore.
- Company F's production of Item I:
- Company F's share of total production is \( 5% \) of Rs. 25 crore:
\[
\frac{5}{100} \times 25 = 1.25 \, \text{crore}
\]
- The ratio of production between items I and II for Company F is \( 1:4 \).
- The share of production for Item I is \( \frac{1}{5} \times 1.25 \, \text{crore} = 0.25 \, \text{crore} \).
- Company D's production of Item II:
- Company D's share of total production is \( 8% \) of Rs. 25 crore:
\[
\frac{8}{100} \times 25 = 2 \, \text{crore}
\]
- The ratio of production between items I and II for Company D is \( 3:5 \).
- The share of production for Item II is \( \frac{5}{8} \times 2 \, \text{crore} = 1.25 \, \text{crore} \).
- To calculate the percentage:
We need to find what percent the cost of production of Item I by Company F is of the cost of production of Item II by Company D. The percentage is given by:
\[
\frac{\text{Cost of production of Item I by Company F}}{\text{Cost of production of Item II by Company D}} \times 100 = \frac{0.25}{1.25} \times 100 = 20%
\]
Thus, the correct answer is 20%.
