Comprehension
A management institute was established on January 1, 2000 with 3, 4, 5, and 6 faculty members in the Marketing, Organisational Behaviour (OB), Finance, and Operations Management (OM) areas respectively, to start with. No faculty member retired or joined the institute in the first three months of the year 2000. In the next four years, the institute recruited one faculty member 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 diagram below gives the area-wise average age (in terms of number of completed years) of faculty members as on April 1 of 2000, 2001, 2002, and 2003.
Question: 1
From which area did the faculty member retire?
From which area did the faculty member retire?
Show Hint
Use sum of ages = average x number of members. If nobody joins or leaves in a year, the total age of an area rises by exactly the number of members; a joiner adds 25, a retiree removes his/her age.
Updated On: Nov 4, 2026
- OB
- Marketing
- Finance
- OM
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The Correct Option is C
Solution and Explanation
Step 1: Read the chart and get the total age of each area in 2000:
Average ages on April 1 of 2000, 2001, 2002, 2003 are: Marketing 49.33, 44, 45, 46; OB 50.5, 51.5, 52.5, 47.8; Finance 50.2, 49, 45, 46; OM 45, 43, 44, 45.
Initial members: Marketing 3, OB 4, Finance 5, OM 6. So the total ages on April 1, 2000 are: Marketing \(3\times 49.33=148\), OB \(4\times 50.5=202\), Finance \(5\times 50.2=251\), OM \(6\times 45=270\).
Step 2: Track each area year by year:
Rule: with no joiner and no retiree, the total age rises by the number of members (everyone is one year older); a joiner adds 25 to the total, a retiree removes his/her age.
Marketing: 2001 average 44. With 4 members the total would be 176 = 148 + 3 + 25. So one person joined in 2001. Then 2002: \(4\times 45=180=176+4\) and 2003: \(4\times 46=184=180+4\). No retirement.
OB: 2001: \(4\times 51.5=206=202+4\), 2002: \(4\times 52.5=210=206+4\) (no change in members). 2003: \(5\times 47.8=239=210+4+25\), so one person joined in 2003. No retirement.
OM: 2001: \(7\times 43=301=270+6+25\), so one person joined in 2001. 2002: \(7\times 44=308=301+7\); 2003: \(7\times 45=315=308+7\). No retirement.
Finance: 2001 average 49. With no change the total would be \(251+5=256\) (average 51.2); with only a joiner it would be \((256+25)/6\approx 46.8\). Neither equals 49. With only a retirement the 4 remaining members have total \(256-60=196=4\times 49\), which matches: a member aged 60 on April 1, 2001 (59 a year earlier) retired from Finance.
Step 3: Check the Finance joiner:
2002: \(5\times 45=225=196+4+25\), so a new member joined Finance in 2002. 2003: \(5\times 46=230=225+5\). Everything is consistent, and the one retirement at age 60 is in Finance.
Final Answer:
The correct option is (3): Finance
Average ages on April 1 of 2000, 2001, 2002, 2003 are: Marketing 49.33, 44, 45, 46; OB 50.5, 51.5, 52.5, 47.8; Finance 50.2, 49, 45, 46; OM 45, 43, 44, 45.
Initial members: Marketing 3, OB 4, Finance 5, OM 6. So the total ages on April 1, 2000 are: Marketing \(3\times 49.33=148\), OB \(4\times 50.5=202\), Finance \(5\times 50.2=251\), OM \(6\times 45=270\).
Step 2: Track each area year by year:
Rule: with no joiner and no retiree, the total age rises by the number of members (everyone is one year older); a joiner adds 25 to the total, a retiree removes his/her age.
Marketing: 2001 average 44. With 4 members the total would be 176 = 148 + 3 + 25. So one person joined in 2001. Then 2002: \(4\times 45=180=176+4\) and 2003: \(4\times 46=184=180+4\). No retirement.
OB: 2001: \(4\times 51.5=206=202+4\), 2002: \(4\times 52.5=210=206+4\) (no change in members). 2003: \(5\times 47.8=239=210+4+25\), so one person joined in 2003. No retirement.
OM: 2001: \(7\times 43=301=270+6+25\), so one person joined in 2001. 2002: \(7\times 44=308=301+7\); 2003: \(7\times 45=315=308+7\). No retirement.
Finance: 2001 average 49. With no change the total would be \(251+5=256\) (average 51.2); with only a joiner it would be \((256+25)/6\approx 46.8\). Neither equals 49. With only a retirement the 4 remaining members have total \(256-60=196=4\times 49\), which matches: a member aged 60 on April 1, 2001 (59 a year earlier) retired from Finance.
Step 3: Check the Finance joiner:
2002: \(5\times 45=225=196+4+25\), so a new member joined Finance in 2002. 2003: \(5\times 46=230=225+5\). Everything is consistent, and the one retirement at age 60 is in Finance.
Final Answer:
The correct option is (3): Finance
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Question: 2
Professors Naresh and Devesh, two faculty members in the Marketing area, who have been with the Institute since its inception, share a birthday, which falls on 20th November. One was born in 1947 and the other one in 1950. On April 1 2005, what was the age of the third faculty member, who has been in the same area since inception?
Professors Naresh and Devesh, two faculty members in the Marketing area, who have been with the Institute since its inception, share a birthday, which falls on 20th November. One was born in 1947 and the other one in 1950. On April 1 2005, what was the age of the third faculty member, who has been in the same area since inception?
Show Hint
Marketing started with 3 members whose average age on April 1, 2000 was 49.33, so their ages add up to 148. Subtract the two known ages (completed years on April 1, 2000).
Updated On: Nov 4, 2026
- 52
- 50
- 51
- 47
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The Correct Option is A
Solution and Explanation
Step 1: Total age of the three original Marketing members on April 1, 2000:
Average age in 2000 = 49.33 (chart) for 3 members, so the total is \(3\times 49.33 = 148\).
Step 2: Ages of Naresh and Devesh on April 1, 2000:
Birthday is 20 November, so on April 1, 2000 the person born in 1947 had completed \(1999-1947=52\) years (he turned 52 on 20 Nov 1999). The person born in 1950 had completed \(1999-1950=49\) years.
Step 3: Age of the third member:
On April 1, 2000: \(148-52-49=47\) years.
Step 4: Age on April 1, 2005:
Five years later, the third member has completed \(47+5=52\) years.
Final Answer:
The correct option is (1): 52
Average age in 2000 = 49.33 (chart) for 3 members, so the total is \(3\times 49.33 = 148\).
Step 2: Ages of Naresh and Devesh on April 1, 2000:
Birthday is 20 November, so on April 1, 2000 the person born in 1947 had completed \(1999-1947=52\) years (he turned 52 on 20 Nov 1999). The person born in 1950 had completed \(1999-1950=49\) years.
Step 3: Age of the third member:
On April 1, 2000: \(148-52-49=47\) years.
Step 4: Age on April 1, 2005:
Five years later, the third member has completed \(47+5=52\) years.
Final Answer:
The correct option is (1): 52
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Question: 3
In which year did the new faculty member join the Finance area?
In which year did the new faculty member join the Finance area?
Show Hint
Compare the actual total age of Finance (average x members) each year with what it would be if nobody joined or left.
Updated On: Nov 4, 2026
- 2000
- 2002
- 2001
- 2003
Show Solution
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The Correct Option is B
Solution and Explanation
Step 1: Total ages in Finance:
Finance had 5 members on April 1, 2000 with average 50.2, so total \(=251\). The chart averages for 2001, 2002, 2003 are 49, 45, 46.
Step 2: 2001:
Try each possibility for 2001. No change: total \(251+5=256\), average 51.2. Only a joiner: \((256+25)/6\approx 46.8\). Both a retiree and a joiner: 5 members and total \(256-r+25\) for the retiree's age r, which would need r = 36, impossible for a retiree aged 60. Only a retiree (aged 60 on April 1, 2001): 4 members with total \(256-60=196=4\times 49\), which matches. So nobody joined Finance in 2001; the one retirement happened here.
Step 3: 2002:
With 4 members continuing, the total would be \(196+4=200\) (average 50). The actual average is 45; with a joiner of age 25 the total is \(196+4+25=225\) for 5 members, and \(225/5=45\). This matches.
Step 4: 2003:
\(225+5=230\), and \(230/5=46\), which matches the chart with no further change. So the new Finance member joined on April 1, 2002.
Final Answer:
The correct option is (2): 2002
Finance had 5 members on April 1, 2000 with average 50.2, so total \(=251\). The chart averages for 2001, 2002, 2003 are 49, 45, 46.
Step 2: 2001:
Try each possibility for 2001. No change: total \(251+5=256\), average 51.2. Only a joiner: \((256+25)/6\approx 46.8\). Both a retiree and a joiner: 5 members and total \(256-r+25\) for the retiree's age r, which would need r = 36, impossible for a retiree aged 60. Only a retiree (aged 60 on April 1, 2001): 4 members with total \(256-60=196=4\times 49\), which matches. So nobody joined Finance in 2001; the one retirement happened here.
Step 3: 2002:
With 4 members continuing, the total would be \(196+4=200\) (average 50). The actual average is 45; with a joiner of age 25 the total is \(196+4+25=225\) for 5 members, and \(225/5=45\). This matches.
Step 4: 2003:
\(225+5=230\), and \(230/5=46\), which matches the chart with no further change. So the new Finance member joined on April 1, 2002.
Final Answer:
The correct option is (2): 2002
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Question: 4
What was the age of the new faculty member, who joined the OM area, as on April 1, 2003?
What was the age of the new faculty member, who joined the OM area, as on April 1, 2003?
Show Hint
Find the year the OM joiner arrived (all joiners are 25 on the day they join, April 1), then add the number of years until April 1, 2003.
Updated On: Nov 4, 2026
- 25
- 27
- 26
- 28
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Total ages in OM:
OM had 6 members on April 1, 2000 with average 45, so total \(=270\). The chart averages for 2001, 2002, 2003 are 43, 44, 45.
Step 2: Find the joining year:
If nobody joined in 2001 the total would be \(270+6=276\) and the average \(46\), not 43. With a joiner of age 25 the total is \(270+6+25=301\) for 7 members, and \(301/7=43\). This matches the chart, so the OM joiner came on April 1, 2001.
Step 3: Check later years:
2002: \(301+7=308\), \(308/7=44\). 2003: \(308+7=315\), \(315/7=45\). Both match, so no other change in OM.
Step 4: Age on April 1, 2003:
The new member was 25 on April 1, 2001, so on April 1, 2003 he/she was \(25+2=27\).
Final Answer:
The correct option is (2): 27
OM had 6 members on April 1, 2000 with average 45, so total \(=270\). The chart averages for 2001, 2002, 2003 are 43, 44, 45.
Step 2: Find the joining year:
If nobody joined in 2001 the total would be \(270+6=276\) and the average \(46\), not 43. With a joiner of age 25 the total is \(270+6+25=301\) for 7 members, and \(301/7=43\). This matches the chart, so the OM joiner came on April 1, 2001.
Step 3: Check later years:
2002: \(301+7=308\), \(308/7=44\). 2003: \(308+7=315\), \(315/7=45\). Both match, so no other change in OM.
Step 4: Age on April 1, 2003:
The new member was 25 on April 1, 2001, so on April 1, 2003 he/she was \(25+2=27\).
Final Answer:
The correct option is (2): 27
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