Introduction
Age Problem Quiz 1 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 1. 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
The ratio between the present ages of A and B is 6:7. If B is 4 years old than A. What will be the ratio of the ages of A and B after 4 years?
- A. 65
B. 75
C. 72
D. 70
Sum of ages is 360 years.The ratio of children and parents ages is 2:1.
Total age of parents = [latex]360 \times \frac{1}{3} = 120 [/latex] years
Ratio of wife and husband age is 5:7. Therefore, the age of husband = [latex]120 \times \frac{7}{12} = 70 [/latex]
Hence the age of husband is 70 years.
Q2
The ratio between the present ages of A and B is 6:7. If B is 4 years old than A. What will be the ratio of the ages of A and B after 4 years?
- A. 5:7
B. 7:8
C. 8:7
D. None of these
Let A’s age and B’s age be 6X years and 7X years respectively
Then, 7X – 6X = 4
X = 4
Required ratio = [latex](6X + 4) : (7X + 4) = (6 \times 4 + 4) : (7 \times 4 + 4) = 28 : 32 = 7 : 8[/latex]
Q3
Sush was thrice as old as Poonam 6 years back. Sush will be 5/3 times as old as Poonam 6 years hence. How old is Poonam today?
- A. 20
B. 14
C. 12
D. 15
Let Poonam age 6 years back = x.
Then, Sush age 6 years back = 3x.
[latex](\frac{5}{3}) \times (X + 6 + 6) = (3X + 6 + 6)[/latex]
So 5(x + 12) = 3(3x + 12),
So x = 6.
Poonam Age = (x + 6) years = 12 years
Q4
Present ages of Simmi and Anu are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively, What is Anu’s present age in years?
- A. 20
B. 24
C. 28
D. 35
Let the present ages of Simmi and Anu be 5x years and 4x years respectively
Then, [latex]\frac{[5X + 3]}{[4X + 3]} = \frac {11}{9}[/latex]
x=6
Anu’s present age = 4X = 24 years
Q5
Ten years ago, Khush was thrice as old as Sam was but 10 years hence, he will be only twice as old. Find Khush’s present age?
- A. 30
B. 35
C. 40
D. 36
Let Khush’s present age be x years and Sam’s present age be y years
Then, according to the first condition,
x – 10 = 3(y – 10)
or, x – 3y = -20 ……..(1)
Now. Khush’s age after 10 years = (x + 10) years
Sam’s age after 10 years = (y + 10)
(x + 10) = 2(y + 10)
or, x – 2y = 10 ……..(2)
Solving (1) and (2), we get
x = 70 and y = 30
Khush’s age = 70 years and Sam’s age = 30 years