Multiple choice

The average age of employees in a company increases by 2 years when some experienced professionals join the team. If the average age of the new employees is 5 years more than the average age of the original employees, what is the ratio of the number of original employees to the number of new employees?

  1. 3 : 2

  2. 4 : 3

  3. 4 : 1

  4. 5 : 2

  5. a
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A Correct answer
Explanation

Let n1 be original employees, A1 average age. Total age = n1*A1. Let n2 be new employees, A2 = A1 + 5. New average = (n1*A1 + n2*(A1+5)) / (n1+n2) = A1 + 2. n1*A1 + n2*A1 + 5*n2 = (A1+2)(n1+n2) = n1*A1 + 2*n1 + n2*A1 + 2*n2. 5*n2 = 2*n1 + 2*n2. 3*n2 = 2*n1. n1/n2 = 3/2.

AI explanation

Using the method of alligation on the average ages, the original employees have an average of x, the new employees have an average of x plus 5, and the combined average is x plus 2. The ratio of the number of original employees to new employees is the difference between the new employees' average and the combined average to the difference between the combined average and the original average. This gives (x plus 5 minus (x plus 2)) divided by ((x plus 2) minus x), which equals 3 divided by 2. The ratio is 3 to 2.

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