Introduction
Age Problem Quiz 6 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 6. 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 the present ages of Supriya and her mother is 2:9. The mother's age at the time of Supriya’s birth was 28 years. Find their present ages.
- A. 8 and 36 yrs
B. 10 and 46 yrs
C. 6 and 26 yrs
D. 10 and 52 yrs
Present ratio of ages between Supriya and her mother is 2: 9.
∴ Let the actual ages of Supriya and her mother be 2x and 9x.
The age of her mother at the time of Supriya’s birth was 28 years.
Therefore, the difference between Supriya and her mother's age will always remain 28 years.
∴ 9x – 2x = 28 ⇒ x = 4. Hence their present ages are 8 and 36 yrs.
Q2
The ratio of the present ages of John and Jim is 4:3. Six years hence it will be 5: 4. Find the present ages
- A. 24 yrs and 18 yrs
B. 20 yrs and 15 yrs
C. 12 yrs and 9 yrs
D. 25 yrs and 20 yrs
Present ratio = 4: 3.
∴ Actual ages are 4x and 3x.
So [latex]\frac {(4x+6)}{(3x+6)} = \frac {5}{4} \Rightarrow x = 6[/latex]
So their present ages are 24 yrs and 18 yrs
Q3
Farookh is aged twice more than his son Raunak. After ten years, he would be twice Ronit’s age. What are there present ages?
- A. 10 and 30 years
B. 20 and 60 years
C. 30 and 90 years
D. 40 and 120 years
Let Raunak's present age be x years.
Now the Farookh is given to be twice more i.e. then,
Farookh's present age =(x + 2x) years = 3x years.
As per the question,
[latex] (3x + 10) = \frac {2}{1(x+10)}[/latex]
[latex]\Rightarrow 3x + 10 = 2x + 20 \Rightarrow[/latex] x = 10.
Hence age of Raunak = 10 years and hence his Farookh’s present age is 30 years.
Q4
The sum of ages of five children born at the intervals of four years each is 80 years. Find the age of the youngest child?
- A. 10 years
B. 12 years
C. 6 years
D. 8 years
Let the ages of children be y, (y + 4), (y + 8), (y + 12) and (y + 16) years.
Then, y + (y + 4) + (y + 8) + (y + 12) + (y+ 16) = 80 [latex]\Rightarrow[/latex] 5y = 40 [latex]\Rightarrow[/latex] y = 8.
So the age of the youngest child y = 8 years.
Q5
Akshay is three years older than Bomkesh, who is twice as old as Chintu. If the sum of the ages of Akshay, Bomkesh and Chintu is 53 years, then how old is Bomkesh?
- A. 50 years
B. 30 years
C. 20 years
D. 60 years
Let Chintu's age be x years.
Then, Bomkesh's age = 2x years.
Hence Akshay's age = (2x + 3) years.
∴ (2x + 3) + 2x + x = 53 [latex]\Rightarrow[/latex] 5x = 50 [latex]\Rightarrow[/latex] x = 10.
Hence, Bomkesh's age = 2x = 20 years.