Introduction
Age Problem Quiz 4 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 4. 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
What is John’s present age, if after 10 years his age will be 5 times his age 5 years back.
- A. 6.2 years
B. 7.7 years
C. 8.7 years
D. 10 years
Let John’s present age be x
John’s age before 5 years = (x - 5)
John’s age after 10 years = (x + 10)
We are given that, John’s age after 10 years (x + 10) is 5 times his age 5 years back (x – 5)
Therefore,
(x + 10) = 5 (x – 5)
Solving the equation, we get
x + 10 = 5x – 25
4x = 35
x = 8.75 years
Q2
Rahul is 15 years elder than Rohan. If 5 years ago, Rahul was 3 times as old as Rohan, then find Rahul's present age.
- A. 32.5 years
B. 27.5 years
C. 25 years
D. 24.9 years
Let age of Rohan be y
Rahul is 15 years elder than Rohan = (y + 15).
So Rahul’s age 5 years ago = (y + 15 – 5)
Rohan’s age before 5 years = (y – 5)
5 years ago, Rahul is 3 times as old as Rohan
(y + 15 – 5) = 3 (y – 5)
(y + 10) = (3y – 15)
2y = 25
y = 12.5
Rohan’s age = 12.5 years
Rahul’s age = (y + 15) = (12.5 + 15) = 27.5 years
Q3
One year ago, ratio of Harry and Peter age’s was 5 : 6 respectively. After 4 years, this ratio becomes 6 : 7. How old is Peter?
- A. 25 years
B. 26 years
C. 31 years
D. 35 years
Hint: If ages in the numerical are mentioned in ratio A : B, then A : B will be Ax and Bx.
We are given that age ratio of Harry : Pitter = 5 : 6
Harry’s age = 5x and Peter’s age = 6x
One year ago, their age was 5x and 6x. Hence at present, Harry’s age = 5x +1 and Peter’s age = 6x +1
After 4 years,
Harry’s age = (5x +1) + 4 = (5x + 5)
Peter’s age = (6x +1) + 4 = (6x + 5)
After 4 years, this ratio becomes 6 : 7. Therefore,
[latex]\frac {Harry’s Age}{6} = \frac {Peter’s Age}{7}[/latex]
[latex]\frac {(5x + 5)}{ (6x + 5)} = \frac {6}{7}[/latex]
7 (5x + 5) = 6 (6x + 5)
X = 5
Peter’s present age = (6x + 1) = (6 x 5 + 1) = 31 years
Harry’s present age = (5x + 1) = (5 x 5 + 1) = 26 years
Q4
Age of mother 10 years ago was 3 times the age of her son. After 10 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
We are given that, age of mother 10 years ago was 3 times the age of her son
So, let age of son be x and as mother’s age is 3 times the age of her son, let it be 3x, three years ago.
At present: Mother’s age will be (3x + 10) and son’s age will be (x + 10)
After 10 years: Mother’s age will be (3x + 10) +10 and son’s age will be (x + 10) + 10
Mother’s age is twice that of son
(3x + 10) +10 = 2 [(x + 10) + 10]
(3x + 20) = 2[x + 20]
Solving the equation, we get x = 20
We are asked to find the present ratio.
(3x + 10) : (x + 10) = 70 : 30 = 7 : 3
Q5
Sharad is 60 years old and Santosh is 80 years old. How many years ago was the ratio of their ages 4 : 6?
- A. 10 years
B. 15 years
C. 20 years
D. 25 years
Here, we have to calculate: How many years ago the ratio of their ages was 4 : 6
Let us assume x years ago
At present: Sharad is 60 years and Santosh is 80 years
x years ago: Sharad’s age = (60 – x) and Santosh’s age = (80 – x)
Ratio of their ages x years ago was 4 : 6
[latex]\frac {(60 – x)}{(80 – x)} = \frac {4}{6}[/latex]
6(60 – x) = 4(80 – x)
360 – 6x = 320 – 4x
x = 20
Therefore, 20 years ago, the ratio of their ages was 4 : 6