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In an organisation with three departments i.e. Marketing, Finance and HR, it was decided to shuffle the 70 employees between departments. To make optimum use of resources, the management assesses their capability based on their qualification. 3 employees can work in every department. 7 employees can work in Finance and Marketing only. 10 can work only in HR while the number of employees only in Marketing is double of that in only Finance. Employees in only Finance cannot be less than 10 while employees in Finance and HR only are three times of two less than that of Marketing and HR only. The organisation has employees with all possible combinations of their capabilities.
We know that x+x/2+k+3+3k-6+10+7=70
$$\frac{\ 3x}{2}$$ +4k =56
The solutions possible are x=24, k=5 and x=32 and k=2. But if k=2 then, only finance and hr would have 0. This is not possible as the question states that there exists employees in all possible combinations.
The number of employees in only marketing and HR is 5.
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