Introduction
Age Problem Quiz 8 are most frequently appearing questions in various competitive exams that include Quantitative Aptitude section. By analyzing the equations from the given data and assuming the unknown values, the age problems are solved.
Algebra is a very powerful branch of Mathematics which can be used to solve the Age Problem Quiz 8. Algebra helps in transforming word problems into mathematical expressions in the form of equations using variables to denote unknown quantities or parameters and thus, providing numerous techniques to solve these mathematical equations and hence, determining the answer to the problem. Identifying key information, organizing information, using mathematical expressions to assume unknown values and thus solving mathematical expressions for the unknown values will help us identify solutions.
Calculate Present age:
If the current age of a person be X, then
- age after n years = X + n
- age n years ago = X – n
- n times the age = nX
- If ages in the numerical are mentioned in ratio A : B, then A : B will be AX and BX
Q1
Father is four times the age of his daughter. If after 5 years, he would be threee times of daughter’s age, then further after 5 years, how many times he would be of his daughter’s age?
- A. 1.5 times
B. 2 times
C. 2.5 times
D. 3 times
Let the daughter's age be x and father's age be 4x.
So as per question, 4x + 5 = 3(x + 5). So x = 10.
Hence present age of daughter is 10 years and present age of father is 40 years.
So after 5 + 5 = 10 years, daughter age would be 20 years and father’s age would be 50 years.
Hence father would be [latex]\frac {50}{20}[/latex] = 2.5 times of daughter’s age.
Q2
What is Aman's present age, if after 20 years his age will be 10 times his age 10 years back?
- A. 6.2 years
B. 7.7 years
C. 13.3 years
D. 10 years
Let Aman's present age be x
Aman's age before 10 years = (x - 10)
Aman's age after 20 years = (x + 20)
We are given that, Aman's age after 20 years (x + 20) is 10 times his age 10 years back (x – 10)
Therefore, (x + 20) = 10 (x – 10)
Solving the equation, we get x + 20 = 10x – 100
9x = 120, x = 13.3 years
Q3
Nisha is 15 years elder to Romi. If 5 years ago, Nisha was 3 times as old as Romi, then find Nisha’s present age.
- A. 32.5 years
B. 27.5 years
C. 25 years
D. 24.9 years
Let age of Romi be y
Nisha is 15 years elder than Romi = (y + 15). So Nisha's age 5 years ago = (y + 15 – 5).
Romi's age before 5 years = (y – 5)
5 years ago, Nisha is 3 times as old as Romi
(y + 15 – 5) = 3 (y – 5)
(y + 10) = (3y – 15)
2y = 25 ⇒ y = 12.5
Romi's age = 12.5 years
Nisha's age = (y + 15) = (12.5 + 15) = 27.5 years.
Q4
One year ago, the ratio of Honey and Piyush ages was 2: 3 respectively. After five years from now, this ratio becomes 4: 5. How old is Piyush now?
- A. 5 years
B. 25 years
C. 10 years
D. 15 years
We are given that age ratio of Honey: Piyush = 2: 3
Honey’s age = 2x and Piyush’s age = 3x
One year ago, their age was 2x and 3x.
Hence at present, Honey's age = 2x +1 and Piyush's age = 3x +1
After 5 years, Honey’s age = (2x +1) + 5 = (2x + 6)
Piyush's age = (3x +1) + 5 = (3x + 6)
After 5 years, this ratio becomes 4: 5. Therefore,
[latex]\frac{(2x+6)}{(3x+6)} = \frac {4}{5}[/latex]
10x + 30 = 12x + 24 [latex]\Rightarrow[/latex] x = 3
Piyush's present age = (3x + 1) = (3x 3 + 1) = 10 years
Honey's present age = (2x + 1) = (2x 3 + 1) = 7 years
Q5
Ten years ago, the age of mother was three times the age of her son. After ten years, mother’s age will be twice that of his son. Find the ratio of their present ages.
- A. 11 : 7
B. 9 : 5
C. 7 : 4
D. 7 : 3
10 years ago, age of mother was three times the age of her son. Say, the age of son was x and mother's age was 3x.
At present: Mother's age is (3x + 10) and son’s age is (x + 10)
After ten years: Mother's age will be (3x + 10) +10 and son’s age will be (x + 10) + 10. Given that, mother’s age is twice that of son after ten years.
(3x + 10) + 10 = 2 [(x + 10) + 10]
(3x + 20) = 2[x + 20]
Solving the equation, we get x = 20
(3x + 10) : (x + 10) = 70 : 30 = 7 : 3.