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% -
In company A, if the ratio between the number of employees who are graduates in Commerce and Arts is 10:7, then the number of employees who are graduates in Arts in the same Company is:
588
This item combines percentage data with a given ratio. Company A has a total of 2100 employees, with Science = 32%. The remaining employees are split between Commerce and Arts in a stated ratio, and we must find the Arts head-count.
Since Science takes 32%, the Commerce and Arts streams together form 100% − 32% = 68% of the workforce, i.e. 68% × 2100 = 1428 employees. This 1428 is now divided in the ratio Commerce : Arts = 10 : 7, giving 10 + 7 = 17 equal parts.
Arts share = 7/17 × 1428 = 7 × 84 = 588 (because 1428 ÷ 17 = 84 per part).
The same answer follows from the percentage route: Arts as a percentage of the whole = 7/17 × 68% = 28%, and 28% × 2100 = 588, confirming the value.
The value 532 results from taking 7/17 of the full 2100 while forgetting to remove the 32% Science share first. The value 560 corresponds to splitting 1428 in a 10 : 8 ratio (i.e. 8/18 of 1428) instead of 10 : 7. The value 616 is the Commerce share taken by mistake, since 10/17 × 1428 would relate to Commerce, not Arts — but note 616 specifically comes from an off-by-one part error; the exact Arts figure is 588.
Correct answer: 588
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