The following table shows (i) the percentage distribution of total number of products P and Q produced by six companies A-F. (ii) the ratio of P to Q, and (iii) the percentage sale of P and Q. Total number of products P and Q produced by these companies is 8 lakhs. Based on the data in the table answer the questions: Company-wise distribution and sale of productsCompany Distribution (%) of P and Q Ratio Sale (%) P Q P Q A 24% 5 3 65% 62% B 18% 5 4 56% 78% C 15% 2 3 72% 66% D 28% 3 4 75% 60% E 7% 4 3 64% 55% F 8% 3 2 50% 48%
What is the difference between the sale of number of products P and products Q by company E?
7280
Analyzing Product Sales Difference for Company E
The question asks us to calculate the difference between the number of products P and products Q sold by company E, using the data provided in the table. The total production of products P and Q across all six companies (A to F) is given as 8 lakhs, which is \(8,00,000\).
Understanding Company E's Data
From the table, we extract the relevant information for Company E:
- Percentage distribution of Total P and Q: 7%
- Ratio of P to Q: 4:3
- Percentage Sale of P: 64%
- Percentage Sale of Q: 55%
Step-by-Step Calculation
1. Calculate Total Production by Company E
Company E's share of the total production of 8,00,000 is 7%.
\[ \text{Total Production by E} = 7\% \text{ of } 8,00,000 \] \[ = \frac{7}{100} \times 8,00,000 = 0.07 \times 8,00,000 = 56,000 \]So, company E produced a total of 56,000 products (P and Q combined).
2. Calculate Production of P and Q Individually by Company E
The ratio of P to Q production for company E is 4:3. The total parts in this ratio are \(4 + 3 = 7\).
To find the number of P produced:
\[ \text{Production of P by E} = \frac{4}{7} \times \text{Total Production by E} \] \[ = \frac{4}{7} \times 56,000 = 4 \times \left(\frac{56,000}{7}\right) = 4 \times 8,000 = 32,000 \]To find the number of Q produced:
\[ \text{Production of Q by E} = \frac{3}{7} \times \text{Total Production by E} \] \[ = \frac{3}{7} \times 56,000 = 3 \times \left(\frac{56,000}{7}\right) = 3 \times 8,000 = 24,000 \]Thus, company E produced 32,000 units of product P and 24,000 units of product Q.
3. Calculate Number of Products P Sold by Company E
Company E sold 64% of the product P it produced.
\[ \text{Number of P Sold by E} = 64\% \text{ of Production of P by E} \] \[ = \frac{64}{100} \times 32,000 = 0.64 \times 32,000 = 20,480 \]Company E sold 20,480 units of product P.
4. Calculate Number of Products Q Sold by Company E
Company E sold 55% of the product Q it produced.
\[ \text{Number of Q Sold by E} = 55\% \text{ of Production of Q by E} \] \[ = \frac{55}{100} \times 24,000 = 0.55 \times 24,000 = 13,200 \]Company E sold 13,200 units of product Q.
5. Calculate the Difference in Sales (P vs Q) for Company E
We need to find the difference between the number of products P sold and products Q sold by company E.
\[ \text{Difference} = \text{Number of P Sold by E} - \text{Number of Q Sold by E} \] \[ = 20,480 - 13,200 = 7,280 \]The difference in the sale of products P and Q by company E is 7,280.
Summary of Calculations for Company E's Sales Difference
| Metric | Value | Explanation/Calculation |
|---|---|---|
| Total Production (P+Q) by E | 56,000 | 7% of 8,00,000 |
| Production of P by E | 32,000 | (4/7) of 56,000 |
| Production of Q by E | 24,000 | (3/7) of 56,000 |
| Number of P Sold by E | 20,480 | 64% of 32,000 |
| Number of Q Sold by E | 13,200 | 55% of 24,000 |
| Difference in Sales (P - Q) | 7,280 | 20,480 - 13,200 |
Revision Table: Key Data Interpretation Skills
| Skill | Importance in this Problem | Application |
|---|---|---|
| Percentage Calculation | Converting percentages to actual numbers (total production, sales). | Used to find production by E and sold units of P and Q. |
| Ratio Analysis | Dividing a total quantity based on a given ratio. | Used to find individual production of P and Q from their combined total. |
| Table Reading | Extracting correct percentages and ratios for Company E. | Foundation for all calculations. |
| Arithmetic Operations | Performing multiplication, division, and subtraction accurately. | Carrying out all steps of the calculation process. |
Additional Information: Insights from Business Data
Data tables like this provide valuable insights into a company's operations. By breaking down total production by company and product type, and then looking at sales rates, we can understand efficiency and market reach.
- A high sales percentage for a product generally indicates strong demand or effective sales strategies.
- Comparing sales percentages between products (like P and Q for company E) can highlight which product is performing better in terms of sales volume relative to its production.
- Understanding the total production distribution helps in seeing the contribution of each company to the overall output.
These types of calculations are fundamental in business analysis, market research, and financial reporting to assess performance and make informed decisions.
Important Questions from Tabulation
The table shows District-wise data of a number of primary school teachers posted in schools of a city.
Study the table and answer the question:
District
Male teachers
Female teachers
East
1650
2375
North
1075
2651
West
1280
1520
South
1170
1085
Central
690
859
What is the difference between the total number of male teachers in the districts East, North, West taken together and the total number of female teachers in the districts East and South?Table shows income (in Rs. ) received by 4 employees of a company during the month of December 2020 and all their income sources.
Source
Amit
Suresh
Nitin
Varun
Salary
35000
38500
29000
42000
Arrears
6000
6300
5000
7500
Bonus
1000
1100
1000
1240
Overtime
1800
1950
1400
1500
What is the ratio of salary of Varun to his income other than salary?Study the table and answer the question:
Income (Rs.)
No. of persons
Less than 200
12
Less than 250
26
Less than 300
34
Less than 350
40
Less than 400
50
What is the percentage of persons earning Rs. 250 or more?The following table shows the annual profit of a company (in Rs. lakh).
2014-2015
2015-2016
2016-0217
2017-2018
2018-2019
625
690
725
775
815
The period which has the maximum percentage increase in profit over the previous year is:
The table given below shows the number of persons participating in a survey from 6 different states.
States Persons S1 100 S2 200 S3 400 S4 500 S5 600 S6 800 What is the ratio of number of person participating in a survey from state S3 to the number of person participating in a survey from state S4?
