Question Details

Read the given information carefully and answer the related questions:


Seven persons was born on same date and same month but in different years – 1955, 1967, 1973 1980, 1987, 1991, 2003. Consider the base year 2024 to calculate the ages.

L’s age is multiple of 3. Three persons were born between L and Q. Number of persons born before Q is same as the number of persons born after P . Difference between the age of Q and K is 12 years. M is 7 years older to N. N is younger to O.

What is the total age of K and N?

Options

A

84 years

B

65 years

C

81 years

D

58 years

E

70 years

Show Answer

Correct Answer :

Option E

70 years

Solution :

The correct option is 70 years.


Let's determine the age of each person as of the base year 2024 by subtracting their birth year from 2024:

1955: 2024 - 1955 = 69 years old
1967: 2024 - 1967 = 57 years old
1973: 2024 - 1973 = 51 years old
1980: 2024 - 1980 = 44 years old
1987: 2024 - 1987 = 37 years old
1991: 2024 - 1991 = 33 years old
2003: 2024 - 2003 = 21 years old


Arranging the birth years in chronological order with their calculated ages:

1. 1955 (Age: 69)
2. 1967 (Age: 57)
3. 1973 (Age: 51)
4. 1980 (Age: 44)
5. 1987 (Age: 37)
6. 1991 (Age: 33)
7. 2003 (Age: 21)


Now, let's step through the given clues:

1. "L’s age is multiple of 3."
The ages that are multiples of 3 are: 69, 57, 51, 33, and 21.


2. "Three persons were born between L and Q."
This means there are exactly 3 positions between L and Q in the ordered list.
- If L is at position 1 (1955), Q must be at position 5 (1987).
- If L is at position 2 (1967), Q must be at position 6 (1991).
- If L is at position 3 (1973), Q must be at position 7 (2003).
- If L is at position 6 (1991), Q must be at position 2 (1967).
- If L is at position 7 (2003), Q must be at position 3 (1973).


3. "Number of persons born before Q is same as the number of persons born after P."
This symmetry implies that the position of P from the bottom is the same as the position of Q from the top.


4. "Difference between the age of Q and K is 12 years."
Let's check the pairs of ages with a difference of 12 years:
- 69 - 57 = 12
- 44 - 32 (Not available)
- 33 - 21 = 12
So the age pairs with a 12-year difference are (69, 57) and (33, 21).


Let's evaluate the candidate positions for Q:
- If Q is born in 1987 (Age 37): No person has an age with a 12-year difference from 37 (37 + 12 = 49, 37 - 12 = 25). Thus, Q cannot be born in 1987.
- If Q is born in 1991 (Age 33): Then K's age must be 21 (born in 2003).
With Q in 1991 (position 6), L must be in 1967 (position 2, age 57, which is a multiple of 3).
Since Q is at position 6 (5 people born before Q), P must be at position 2 (5 people born after P). But position 2 is already occupied by L, so this case is invalid.


- If Q is born in 1973 (Age 51): No person has an age with a 12-year difference from 51 (51 + 12 = 63, 51 - 12 = 39). Invalid.
- If Q is born in 1967 (Age 57): Then K must be born in 1955 (Age 69, since 69 - 57 = 12).
With Q in 1967 (position 2):
L must be born in 1991 (position 6, age 33, which is a multiple of 3).
Number of persons born before Q (position 2) is 1. Thus, number of persons born after P must be 1, placing P at position 6 (1991). But position 6 is occupied by L. Invalid.


- If Q is born in 2003 (Age 21):
Then K must be born in 1991 (Age 33, since 33 - 21 = 12).
Three persons between L and Q means L is born in 1973 (position 3, age 51, which is a multiple of 3).
Q is at position 7 (6 persons born before Q), so P must be at position 1 (1955, 6 persons born after P).


Let's check the remaining people (M, N, O) for positions 1967, 1980, 1987:
5. "M is 7 years older to N."
Looking at the remaining ages (57, 44, 37):
44 - 37 = 7 years.
Therefore, M's age is 44 (born in 1980) and N's age is 37 (born in 1987).


6. "N is younger to O."
The remaining spot (1967, age 57) goes to O.
O (57) is older than N (37), which fits "N is younger to O".


Final person-to-birth year and age mapping:
- 1955: P (Age 69)
- 1967: O (Age 57)
- 1973: L (Age 51)
- 1980: M (Age 44)
- 1987: N (Age 37)
- 1991: K (Age 33)
- 2003: Q (Age 21)


We are asked for the total age of K and N:

Total age=Age of K+Age of N

Total age=33+37=70 years


Thus, the total age of K and N is 70 years.

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