# Aptitude - Problems on Ages - Discussion

*Directions to Solve*

Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and

- Give answer (A) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.
- Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
- Give answer(E) if the data in both Statements I and II together are necessary to answer the question.

Average age of employees working in a department is 30 years. In the next year, ten workers will retire. What will be the average age in the next year? | |

I. | Retirement age is 60 years. |

II. | There are 50 employees in the department. |

I. Retirement age is 60 years.

II. There are 50 employees in the department.

Average age of 50 employees = 30 years.

Total age of 50 employees = (50 x 30) years = 1500 years.

Number of employees next year = 40.

Total age of 40 employees next year (1500 + 40 - 60 x 10) = 940.

Average age next year = | 940 | years = 23 | 1 | years. |

40 | 2 |

Thus, I and II together give the answer. So, correct answer is (E).

There are 50 employees working in the department, and their average age is 30 years.

So their total age will be 50* 30=1500yrs.

Next year 10 employee will leave the department meaning that their present age is 59 years and so as those 10 employee are leaving next year, their age will be 60yrs, so the total age will be 60'-10=600.

Now the difference between the total age of employees before and after will be 1500-600=900yrs.

Now the total age of the remaining 40 employees will be 40*1=40yrs.

Since both of these conditions are considered to be a year after it would be 900+40=940yrs.

And the average age will be 940/40=23.5yrs.

50*30 + 50 = 1550.

10 employees retire then;

10*60 = 600,

So leftover total ages and leftover total employees;

950/40 = 23.75.

Current year : 23 ----- 23 ----- 23 ----- 22 ----- 59 ----- 30

Next year : 24 ----- 24 ----- 24 ----- 23 ----- Retired 23.75.

Instead of 50, imagine the same problem with 5 employees and one person retires next year. Paste in your excel and then you will see the logic. The original calculation given as an answer is wrong. During the current year, there are 10 people age 59. Only then next year, their age will become 60 and so the 10 people can be retired. Also, since there is the rest 40 employee's ages will also increase one for each, so that is 40*1= 40 years.

Current year:

When avg is 30 for 50 employees, then 30 * 50 = 1500.

There are 10 people age 59, so next year when their age increases by 1, they will retire. so 10*50 = 590.

Next year:

There will be 40 Empoyees left. So left outage is 1500-590+ 40 ( every employees age has increase by 1).

= 950.

Collective age is 40 employee is 950, so average is 950/5= 23.75.

By adding 40 to 1500, it's already excluded 10 employees and then subtracted the ages of those 10 retiring employees with their added ages (60*10 instead of 59*10) thus leading to 10 more years of subtraction.

Here, 40 is the number of employees not the age. How we are adding 40 to 1500. Can any one explain the purpose of 40 step wise step?

Total age of 50 employees = 50 * 30 = 1500,

After one year total no of employees = 40,

10 employees with age of 60 will retire after 1 year.

So total age of 10 employees = 600,

After 1-year remaining employees age = 1500 + 40 = 1540.

Total age after 1 year = 1540 - 600 = 940.

Avrg = 940/40 = 47/2.