In a company, the ratio of the male to female employees is7:9 and the ratio of the graduates to post graduates employeesis 4:5. Find the total number of employees if the differencebetween the number of male employees and the number ofgraduate employees is 2.A) 288B) 264C) 250D) 294E) 312
Question
In a company, the ratio of the male to female employees is7:9 and the ratio of the graduates to post graduates employeesis 4:5. Find the total number of employees if the differencebetween the number of male employees and the number ofgraduate employees is 2.A) 288B) 264C) 250D) 294E) 312
Solution
Let's solve this step by step:
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Let's assume the number of male employees is 7x and the number of female employees is 9x. So, the total number of employees is 7x + 9x = 16x.
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Similarly, let's assume the number of graduate employees is 4y and the number of postgraduate employees is 5y. So, the total number of employees is also 4y + 5y = 9y.
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From the above two points, we can say that 16x = 9y.
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According to the problem, the difference between the number of male employees and the number of graduate employees is 2. So, we can write the equation as 7x - 4y = 2.
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Now, we have two equations (16x = 9y and 7x - 4y = 2) and two variables (x and y). We can solve these equations simultaneously to find the values of x and y.
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By solving these equations, we get x = 18 and y = 32.
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Substituting x = 18 into the equation 16x = 9y, we get the total number of employees as 16*18 = 288.
So, the total number of employees in the company is 288. Therefore, the answer is A) 288.
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