Introduction
Age Problem Quiz 3 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 3. 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 ages of A and B are in the ratio of 8 : 5 respectively. After 5 years the ratio of their ages will be 7:5. What is the difference in years between their ages.
- A. 7 years
B. 3 years
C. 6 years
D. 2 years
A:B
= 8:5
[latex] \Rightarrow [/latex] 16:10
After 5 years
21:15 = 7:5
16-10 = 6 years
Q2
The present ages of three colleague's are in proportions 3 : 5 : 7. Four years ago, the sum of their ages was 48. find their present ages (in years) ?
- A. 12, 20 and 28 years
B. 13, 15 and 23 years
C. 11, 16 and 19 years
D. 20, 24 and 27 years
Let the present age of three colleague's are : 3x, 5x and 7x
(3x – 4) + (5x – 4) + (7x – 4) = 48.
15x – 12 = 48 [latex]\Rightarrow[/latex] 15x = 60 [latex]\Rightarrow[/latex] x = 4.
Their present ages are 12 years, 20 years and 28 years respectively.
Hence, option A is correct.
Q3
The ratio of the Mother's age to her daughter's age is 9 : 5. The product of their ages is 1125. The ratio of their ages after five years will be :
- A. 1:3
B. 2:3
C. 3:4
D. 5:3
Let the present ages of Mother and daughter be 9x and 5x respectively.
[latex]9x × 5x = 1125 \Rightarrow 45{x}^{2} = 1125 \Rightarrow {x}^{2} = 25 \Rightarrow x = 5.[/latex]
Required ratio = (9x + 5) : (5x + 5) ⇒ 50 : 30 [latex]\Rightarrow[/latex] 5 : 3.
Hence, option D is correct.
Q4
The ratio of the present ages of two Friends is 2 : 3 and six years back, the ratio was 1 : 3. What will be the ratio of their ages after 4 years ?.
- A. 1:3
B. 3:4
C. 2:3
D. 3:5
Let the present ages of the two Friends be 2x and 3x respectively.
Then, [latex]\frac {2x – 6}{3x – 6} = \frac {1}{3}[/latex]
[latex] \Rightarrow 6x – 18 = 3x – 6 \Rightarrow 3x = 12 \Rightarrow x = 4. [/latex]
So, required ratio = [latex] (2x + 4) : (3x + 4) \Rightarrow 12 : 16 \Rightarrow 3 : 4. [/latex]
Hence, option B is correct.
Q5
The total ages of Ankit, Narendra and Satendra is 96 years. Five years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Satendra?
- A. 21 years
B. 32 years
C. 41 years
D. 53 years
Let the ages of Ankit, Narendra and Satendra 5 years ago be 2x, 3x and 4x years respectively.
So, total of their present ages will be,
(2x + 5) + (3x +5) + (4x + 5) = 96
9x + 15 = 96
9x = 81
x = 9.
So, the present age of Satendra = 4x + 5 = 4 × 9 + 5 = 41 years.
Hence, option C is correct.