In the miscellaneous section of Quantitative Aptitude, "Ages" is one of the important topics.
To make the chapter easy for you all, we are providing you with all some Basic Concept and Tricks on Age-Related Questions which will surely make the chapter easy for you all.
Have a look at the following questions:-
Question. 1: The age of the father 3 years ago was 7 times the age of his son. At present, the father’s age is five times that of his son. What are the present ages of the father and the son?
Solution: Let the present age of son = x yrs
Then, the present age of father = 5xyr
3 years ago,
7(x – 3)= 5x – 3
Or, 7x – 21 =5x – 3
Or, 2x =18
x = 9 yrs
Therefore, the son’s age = 9 years
Father’s age = 45 years
Question. 2: At present, the age of the father is five times the age of his son. Three years hence, the father’s age would be four times that of his son. Find the present ages of the father and the son.
Solution: Let the present age of son = x yrs
Then, the present age of father = 5x yrs
3 yrs hence,
4(x+3)= 5x+3
Or, 4x + 12=5x +3
x= 9yrs.
Therefore, son’s age = 9 yrs and father’s age = 45 yrs
Question. 3: Three years earlier, the father was 7 times as old as his son. Three years hence, the father’s age would be four times of his son. What are the present ages of the father and the son?
Solution: Let the present age of son = x yrs and the present age of father = y yrs
3 yrs earlier, 7(x – 3) = y – 3
7x – y =18………….(i)
3 yes hence, 4(x+3) = y +3
4x +12 = y + 3
4x – y = – 9 …………(ii)
Solving (1) & (2) we get, x = 9 yrs & y =45 yrs
Question. 4: The sum of the ages of a mother and her daughter is 50 yrs. Also 5 yrs ago, the mother’s age was 7 times the age of the daughter. What are the present ages of the mother and the daughter?
Solution: Let the age of the daughter be x yrs.
Then, the age of the mother is (50x – x)yrs
5 yrs ago, 7(x – 5) = 50 – x – 5
Or, 8x = 50 – 5 +35 = 80
x =10
Therefore, the daughter’s age = 10 yrs and mother’s age = 40yrs
Question. 5: The sum of the ages of a son and father is 56 yrs. After 4 yrs, the age of the father will be three times that of the son. What is the age of the son?
Solution: Let the age of the son be x yrs.
Then, the age of the father is (56 – x) yrs.
After 4 yrs, 3(x+4) = 56 – x +4
Or, 4x =56 +4 – 12 = 48
x = 12 yrs
Thus, the son’s age = 12 yrs
Note: Just try to make two equations and then solve them to get your answer.
Question 6: A man’s age is 133(1/3)% of what it was 8 years ago, but 80% of what it will be after 8 years. What is his present age?
Solution: Let the present age be X years.
Then 133(1/3)% of (X-8) = X and 80%(X+8) = X
So, 133(1/3)% of (X-8) = 80%(X+8)
4(X-8)/3 = 4(X+8)/5
5(X-8) = 3(X+8)
2X = 64
X = 32
Shortcut: You don’t need to solve both equations. Solve any equation you will get the answer.
133(1/3)% of (X-8) = X
4(X-8)/3 = X
4X-32 = 3X
X = 32 years.
Question 7: The present age of Romila is one-fourth that of her father. After 6 years the father’s age will be twice the age of Kapil. If Kapil celebrated his fifth birthday 8 years ago. What is Romila’s present age?
Solution: Let the present age of Romila is X, then Father’s age = 4X
6 years hence,
father’s age = 4X+6
2 (Age of Kapil) = 4X+6
Age of Kapil = 2X+3
Present age of Kapil = 2X+3-6 = 2X-3
Kapil celebrated his 5th birthday 8 years ago
So, Present age of Kapil is 5+8 = 13 years
2X-3 = 13
2X = 16
X = 8years.
Shortcut approach: Kapil celebrated his 5th birthday 8 years ago.
The present age of Kapil = 13
After 6years, father’s age will be twice of the Kapil.
2x(13+6) = 4X+6
X= 8 years
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