Introduction
Age Problem Quiz 7 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 7. 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 of B’s age six years hence to C’s present age is 3:2. B is thirteen years younger than A. If A’s present age is twice the age of C, then find B’s age, after 5 years?
- A. 22 years
B. 24 years
C. 26 years
D. 20 years
The ratio of B’s age six years hence to C’s present age = 3: 2 (3x, 2x)
Present ages of B to C = 3x - 6, 2x
Present ages of A to C = 2 : 1(2x, x)
Present ages of A, B and C = 4x, 3x - 6, 2x
B = A – 13
A – B = 13
4x – (3x - 6) = 13
4x – 3x + 6 = 13
X = 7
B’s age, after 5 years = 3x – 6 + 5 = 21 – 1 = 20 years
Q2
The average of three persons A, B and C, three years ago was 28 years. While the average ages of A, B, C and D at present is 32 years, then find the age of D, 8 years ago?
- A. 27 years
B. 23 years
C. 25 years
D. 19 years
Total ages of A, B and C three years ago
[latex]\Rightarrow 28 \times 3 [/latex] = 84 years
Total present ages of A, B and C = 84 + 9 = 93 years
Total present ages of A, B, C and D = 32 [latex]\times[/latex] 4 = 128 years
Present age of D = 128 – 93 = 35 years
Age of D, 8 years ago = 35 – 8 = 27 years.
Q3
5 years ago, the ratio of age of A and B is 3: 2. C is 7 years younger than A. The present age of C is 2 times of D’s present age. Find the present age of B, if the age of D, after 6 years is 35 years?
- A. 40 years
B. 42 years
C. 45 years
D. 38 years
5 years ago, the ratio of age of A and B = 3: 2 (3x, 2x)
The present age of A and B = 3x + 5, 2x + 5
Present age of C = Present age of A – 7
Present age of D = 35 – 6 = 29
Present age of C = 2 [latex]\times[/latex] present age of D
[latex]\Rightarrow 2 \times 29 [/latex] = 58 years
Present age of A = 58 + 7 = 65 years
3x + 5 = 65
3x = 60
X = 20
The present age of B = 2x + 5 = 45 years
Q4
After 7 years, the age of Kavi is 2 times the age of Silambu, 8 years ago. Preethi is 5 years elder than Silambu. Find the present age of Kavi, if the present age of Preethi is 30 years?
- A. 25 years
B. 27 years
C. 23 years
D. 21 years
The ratio of age of Kavi’s age after 7 years and Silambu’s age 8 years ago = 2 : 1 (2x, x)
Preethi’s present age = 30 years
Silambu’s present age = 30 – 5 = 25
Silambu’s age 8 years ago = 17
X = 17
2x = 34
After 7 years, the age of Kavi = 34 years
Present age of Kavi = 27 years
Q5
The ratio of present age of A and B is 6: 7. The present age of C is square of half of B’s present age. Find the present age of C, if the age of A after 6 years is 18 years?
- A. 49 years
B. 45 years
C. 41 years
D. 38 years
The ratio of present age of A and B = 6: 7 (6x, 7x)
The present age of C = [latex]{(\frac {B’s present age}{2})}^{2}[/latex]
A’s age after 6 years = 18 years
Present age of A = 12 years
6x = 12
X = 2
Present age of B = 7x = 14 years
Present age of C = [latex]{(\frac {14}{2})}^{2} = {7}^{2}[/latex] = 49 years