Introduction
Age Problem Quiz 9 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 9. 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
4 years ago Harish uncle was 5 times old as Harish. 4 years hence, his uncle’s age would be 3 times that of Harish. Find the present age of Harish and his uncle?
- A. 44 years, 12 years
B. 44 years, 28 years
C. 40 years, 14 years
D. 38 years, 12 years
4 years ago, the ratio of age of Harish uncle to that of Harish
[latex]\Rightarrow[/latex] 5 : 1 (5x, x)
4 years hence, the ratio of age of Harish uncle to that of Harish
[latex]\Rightarrow[/latex] 3 : 1
According to the question,
[latex]\frac{(5x + 8)}{(x + 8)} = (\frac {3}{1})[/latex]
5x + 8 = 3x + 24
5x – 3x = 24 – 8
2x = 16
x = 8
Present age of Harish uncle = 5 [latex]\times[/latex] 8 + 4 = 44
Present age of Harish = 12
Q2
Milky was thrice as old as Vijay 17 years back. How old is Vijay today, if the age of milky, after 10 years will be 45 years?
- A. 32 years
B. 28 years
C. 23 years
D. 35 years
17 years back, the ratio of age of milky and vijay = 3 : 1
Milky’s present age = 45 – 10 = 35
17 yrs back, Milky’s age = 18
3’s = 18
1’s = 6
Now vijay age = 6 + 17 =23 years
Q3
The ratio of father and son‘s age is 8:5. The product of their ages is 2560. The ratio of their ages, 4 years ago is?
- A. 4 : 5
B. 5 : 3
C. 6 : 7
D. 7 : 8
Let their ages is 8x and 5x
Product = [latex]40{x}^{2} = 2560[/latex]
[latex]{x}^{2} = \frac {2560}{40} = 64[/latex]
x = 8
Their ages = 64 : 40
4 years ago = 60 : 36 = 15 : 9 = 5 : 3
Q4
A’s age is 3 times more than B. After 4 years, A’s age would be three and a half times of B’s age. After further 6 years, B’s age would be?
- A. 30 years
B. 28 years
C. 23 years
D. 35 years
B’s present age = x
A’s present age = x + 3x = 4x
4x + 4 = [latex]\frac {7}{2} (x + 4)[/latex]
8x + 8 = 7x + 28
8x – 7x = 28 – 8 = 20
x = 20
After 10 years, the age of B = x + 10 = 30 years
Q5
The difference between the mother and her daughter is 30 years. 4 years hence, the age of mother will be four times that of her daughter. What is the age of the mother?
- A. 32 years
B. 28 years
C. 36 years
D. 42 years
X – mother; y-daughter
x – y = 30
y = x – 30
After 4 Years
x + 4 = 4 (y + 4)
x + 4 = 4 (x – 30 + 4)
x + 4 = 4x – 120 + 16
4 + 104 = 4x – x
3x = 108
X = 36 years