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 E, if the average number of employees who are Graduates in Arts and Commerce is 377, then the number of employees in company E is
1160
Here we must work backwards from an average to find the total workforce N of Company E. The streams again sum to 100%, so the missing percentage is obtained by subtraction, and an "average of two groups" is converted into a total by multiplying by 2.
For Company E the table gives Science = 35% and Commerce = 50%, so Arts = 100% − 35% − 50% = 15%. The problem states that the average number of Arts and Commerce graduates is 377. Since this is the mean of exactly two quantities, their sum is:
Arts + Commerce = 377 × 2 = 754 employees.
Expressed as a fraction of the whole workforce, Arts + Commerce = 15% + 50% = 65% of N. Therefore 65% of N = 754, which gives:
N = 754 ÷ 0.65 = 1160.
A quick check: 15% of 1160 = 174 (Arts) and 50% of 1160 = 580 (Commerce); their average is (174 + 580)/2 = 754/2 = 377, exactly as required.
The value 1120 comes from using a wrong Arts percentage (for example 13% or 17%) so that the combined share is not 65%. The values 1320 and 1360 typically result from treating 377 as the sum rather than the average, or from adding the wrong pair of streams, both of which distort the divisor.
Correct answer: 1160
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