The following table shows the number of employees working in five different companies A-E in December, 2021 along with the percentage distribution of Science, Commerce and Arts Graduates among them. Based on the data in the table, answer the questions that follow. Company-wise Details of Employees Number of Employees Note: (1) Employees of all five companies can be categorised only in three types of Graduates: Science, Commerce and Arts. (2) Some values are missing in the table (indicated by ‘-’) that you are expected to calculate if required.Company Science (%) Commerce (%) Arts (%) A 2100 32% - - B 1400 - 31% 40% C - 30% 30% - D - - 40% 20% E - 35% 50% -
If the number of employees in company D is 3 times the number of employees in Company C and the difference between the number of employees who are Arts Graduates in company D and that in company C is 480, then the number of employees in company C is
2400
This is an algebraic set-up on the same percentage table. We are told the size relationship between two companies and the absolute difference in their Arts graduates, and we must recover the smaller company's size.
Let the number of employees in Company C be C. Then Company D = 3C (three times as many). Using the Arts percentages from the table — Arts is 20% in Company D and 40% in Company C — the Arts head-counts are:
- Arts graduates in D = 20% × 3C = 0.20 × 3C = 0.6C
- Arts graduates in C = 40% × C = 0.4C
The difference between them is given as 480:
0.6C − 0.4C = 0.2C = 480, so C = 480 ÷ 0.2 = 2400.
Verification: with C = 2400, Company D = 7200; Arts in D = 20% × 7200 = 1440 and Arts in C = 40% × 2400 = 960; their difference is 1440 − 960 = 480, exactly as stated.
The value 2880 comes from mistakenly solving for D (3C would give 7200, but a partial error yields 2880-type figures) or using 3C as the difference base. The value 2640 results from mis-adding the Arts percentages, and 1800 comes from reversing the company roles (treating C as the larger firm), which flips the coefficient and changes the divisor.
Correct answer: 2400
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