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Directions for Questions 1 and 2 :
Space Institute which is involved in training and helping students prepare for Management Institute Entrance Exams, was established on January 1, 2004 with 3, 4, 5 and 6 faculty members in the Logical Reasoning (LR), Data Interpretation (Dl), English Language and Quantitative Analysis (QA) areas respectively, to start with. No faculty member retired or joined the institute in the first three months, of the year 2004. In the next four years, the institute recruited faculty members in each of the four areas. All these new faculty members who joined the institute subsequently over the years were 25 years old at the time of their joining the institute. All of them joined the institute on April 1. During these four years, one of the faculty members retired at the age of 60. The following table gives the area-wise average age (in terms of number of completed years) of faculty members as on April 1 of 2004.2005,2006 and 2007.

For question 1 and 2 : The average age of the different groups is in the range of 43 â€“ 55. So whenever
(1) A 25 year old joins the group, the average age of the group dips by around 5 to 6 years
(2) A 60 years old is retired, the average age of the group dips lesser than that in statement (1) above.

Question 1. In which year did the new faculty member join as the faculty of English?
A. 2004
B. 2005
C. 2006
D. 2007

Question 2.Â Â Professor Sharma and Professor Verma, two faculty members in the LR area, who have been with the Institute since its inception, share a birthday, which falls on 30thÂ November. One was born in 1951 and the other one in 1954. On April 1,2009 what would be the age of the third faculty member, who has been in the same area since inception?
A. 47
B. 50
C. 51
D. 52

Read the notes in the beginning of the solution. The average age dips twice first from 2004 to 2005 and then from 2005 to 2006. The dip is more when a 25 years old joins & lesser when somebody retires.

Let the person be X. From the data for 2004, as on April 1, 2004:

(Age of Sharma) + (Age of Verma) + (Age of X) = 49.33 Ã— 3 = 148 years.

Now the sum of ages of Sharma and Verma, as on 1 April 2004 is:

â‡’ the age of X on 1 April 2004 is 47y + 3m + 10d

â‡’ X’s age on 1 April 2009 is â‰¡ 52y + 3m + 10d

Hence, (D) is the correct option.Â­

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