AGES

1.The age of the father 8 years ago was 5 times the age of his son. At present the father’s age is 3 times that of his son. Find the present age of father. 

(a) 48 years

(b) 36 years

(c) 46 years

(d) 58 years 

2.12 years ago, the ratio of the ages of Ram and Rahim is 2 : 3. If the ratio of their present ages is 5 : 6, what will be the total of their present ages. 

(a) 46 years

(b) 42 years 

(c) 44 years 

(d) 48 years 

3. Ten years ago Mohan was thrice as old as Ram was but 10 years hence, he will be only twice as old as Ram. Find Mohan’s present age. 

(a) 72 years

(b) 70 years 

(c) 30 years 

(d) Cannot be determined 

4.The sum of the ages of a mother and her daughter is 50 years. Also 5 years ago, the mother’s age was 7 times the age of the daughter. What are the present ages of the mother and the daughter? 

(a) 46 years

(b) 42 years 

(c) 44 years 

(d) 40 years 

5.The sum of the age of a vineet and a roshan is 56 years. Also, 4 years ago, the roshan age was 3 times the age of the vinnet. The present ages of the vineet :

(a) 15

(b) 16

(c) 17

(d) 18

6.The ratio of A’s and B’s ages is 4 : 5. If the difference between the present age of B and the age of A, 5 years hence is 3, then what is the total of present ages of A and B? 

(a) 68 years

(b) 72 years 

(c) 50 years 

(d) 90 years 

7.If the ages of P and R are added to twice the age of Q, the total becomes 59. If the ages of Q and R are added to thrice the age of P, the total becomes 68. And if the age of P is added to thrice the age of Q and thrice the age of R, the total becomes 108. What is the age of P? 

(a) 15 years

(b) 19 years 

(c) 17 years 

(d) 12 years 

8.The product of the ages of Harish and Seema is 240. If twice the age of Seema is more than Harish’s age by 4 years, what is Seema’s age in years? 

(a) 12 years

(b) 20 years 

(c) 10 years 

(d) 14 years

9.Jayesh is twice as old as Vijay and half as old as Suresh. If the sum of Suresh’s and Vijay’s ages is 85 years, what is Jayesh’s age in years? 

(a) 34

(b) 36

(c) 68

(d) Can not be determined 

10.The ratio of the present ages of a son and his father is 1 : 5 and that of his mother and father is 4 : 5. After 2 years the ratio of the age of the son to that of his mother becomes 3 : 10. What is the present age of the father?

(a) 30 years

(b) 28years 

(c) 37 years 

(d) None Of These 

Quantitative Aptitude

Q1. The ages of Shirish and Kunder are in the ratio of 5 : 6. After 8 years the ratio of their ages will be 7 : 8. What is the difference in their ages?   

(a) 4 years 

(b) 8 years 

(c) 10 years 

(d) 12 years 

(e) None of these

Q2. The total of the ages of a class of 75 girls in 1050, the average age of 25 of them is 12 years and that of another 25 is 16 years. Find the average age of the remaining girls.  

(a) 12 years 

(b) 13 years 

(c) 14 years 

(d) 15 years 

(e) None of these

Q3. The ratio of the ages of Anubha and her mother is 1 : 2. After 6 years the ratio of their ages will be 11 : 20. 9 years before, what was the ratio of their ages?  

(a) 3 : 5 

(b) 2 : 7 

(c) 1 : 4 

(d) 2 : 5

(e) None of these

Q4. The ratio of age of Tina and Rakesh is 9 : 10. 10 years ago the ratio of their ages was 4 : 5. What is the present age of Rakesh?  

(a) 25 years 

(b) 20 years 

(c) 30 years 

(d) 24 years 

(e) None of these

Q5. In a family, mother’s age is twice that of daughter’s age. Father is 10 years older than mother. Brother is 20 years younger than his mother and 5 years older than his sister. What is the age of the father?  

(a) 62 years 

(b) 60 years 

(c) 58 years 

(d) 55 years 

(e) None of these

Q6. A man is 3 years older than his wife and four times as old as his son. If the son becomes 15 years old after 3 years, what is the present age of the wife?  

(a) 60 years 

(b) 51 years 

(c) 48 years 

(d) 45 years 

(e) None of these

Q7. After replacing an old member by a new member, it was found that the average age of five members of a club is same as it was 3 years ago. The difference between the ages of the replaced and the new members is: 

(a) 2 years 

(b) 4 years 

(c) 8 years 

(d) 15 years

(e) None of these

Q8. 7 years ago, the ages (in years) of A and B were in the ratio 4 : 5; and 7 years hence they will be in the ratio 5 : 6. The present age of B is: 

(a) 56 years 

(b) 63 years 

(c) 70 years 

(d) 77 years 

(e) None of these

Q9. The age of the father is 30 years more than the son’s age. Ten years hence, the father’s age will become three times the son’s age that time. What is the son’s present age in years?   

(a) Eight  

(b) Seven 

(c) Five 

(d) Cannot be determined 

(e) None of these 

 

Q10. The ratio of the present age of Manoj to that of Wasim is 3 : 11. Wasim is 12 years younger than Rehana. Rehana’s age after 7 years will be 85 years. What is the present age of Manoj’s father, who is 25 years older than Manoj? 

(a) 43 years

(b) 67 years 

(c) 45 years 

(d) 69 years 

(e) None of these 

Q11. The ratio of the present ages of Ram and Rakesh 6 : 11. 4 years ago, the ratio of their ages was 1 : 2. What will be Rakesh’s age after 5 years?   

(a) 45 years  

(b) 29 years 

(c) 49 years 

(d) Cannot be determined 

(e) None of these 

Q12. Radha’s present age is 3 years less than twice her age 12 years ago. Also the ratio of Raj’s present age of Radha’s present age is 4 : 9. What will be Raj’s age after 5 years?  

(a) 12 years 

(b) 7 years 

(c) 21 years 

(d) Cannot be determined 

(e) None of these 

Q13. Ratio of the ages of Priyanka and Sanjay is 7 : 8. 7 years ago, the ratio of their ages was 6 : 7. What is the present age of Sanjay?  

(a) 56 years 

(b) 77 years 

(c) 30 years 

(d) 14 years 

(e) None of these 

Q14. At present, Meena is eight times her daughter’s age. 8 years from now, the ratio of the ages of Meena and her daughter will be 10 : 3. What is Meena’s present age?  

(a) 32 years 

(b) 40 years  

(c) 36 years 

(d) Cannot be determined 

(e) None of these 

Q15. The ages of Ritu and Karan are in the ratio of 4 : 5. After 10 years, the ratio of their ages will be 6 : 7. What is the difference in their ages?  

(a) 4 years 

(b) 6 years 

(c) 10 years 

(d) 5 years 

(e) None of these 

Quant Quiz

Problems on Age - Solved Examples (Set 6)

26. The product of the ages of Syam and Sunil is $240$. If twice the age of Sunil is more than Syam's age by $4$ years, what is Sunil's age?
A. $16$	B. $14$
C. $12$	D. $10$

answer with explanation

Answer: Option C
Explanation:
Let age of Sunil $=x$ and
age of Syam $=y$

$xy=240\cdots \left(1\right)$

$2x=y+4\Rightarrow y=2x-4\Rightarrow y=2(x-2)\cdots \left(2\right)$

Substituting equation $\left(2\right)$ in equation $\left(1\right)$. We get
$x\times 2(x-2)=240\Rightarrow x(x-2)=\frac{240}{2}\Rightarrow x(x-2)=120\cdots \left(3\right)$

We got a quadratic equation to solve.

Always time is precious and objective tests measure not only how accurate you are but also how fast you are. We can solve this quadratic equation in the traditional way. But it is more easy to substitute the values given in the choices in the quadratic equation (equation $3$) and see which choice satisfy the equation.

Here, option A is $10$. If we substitute that value in the quadratic equation, $x(x-2)=10\times 8$ which is not equal to $120$

Now try option B which is $12$. If we substitute that value in the quadratic equation, $x(x-2)=12\times 10=120$. See, we got that $x=12$

Hence Sunil's age $=12$

(Or else, we can solve the quadratic equation by factorization as,
$x(x-2)=120\Rightarrow x^2-2x-120=0\Rightarrow (x-12)(x+10)=0\Rightarrow x=12\text{or}-10$
Since $x$ is age and cannot be negative, $x=12$

Or by using quadratic formula as
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{2\pm \sqrt{(-2{)}^2-4\times 1\times (-120)}}{2\times 1}=\frac{2\pm \sqrt{4+480}}{2}=\frac{2\pm \sqrt{484}}{2}=\frac{2\pm 22}{2}=12\text{or}-10$

Since age is positive, $x=12$

27. One year ago, the ratio of Sooraj's and Vimal's age was $6:7$ respectively. Four years hence, this ratio would become $7:8$. How old is Vimal?
A. $32$	B. $34$
C. $36$	D. $38$

answer with explanation

Answer: Option C
Explanation:
Let the age of Sooraj and Vimal, $1$ year ago, be $6x$ and $7x$ respectively.

Given that, four years hence, this ratio would become $7:8$
$\Rightarrow (6x+5):(7x+5)=7:8\Rightarrow 8(6x+5)=7(7x+5)\Rightarrow 48x+40=49x+35\Rightarrow x=5$

Vimal's present age
$=7x+1=7\times 5+1=36$

28. The total age of A and B is $12$ years more than the total age of B and C. C is how many year younger than A?
A. $10$	B. $11$
C. $12$	D. $13$

answer with explanation

Answer: Option C
Explanation:
Solution 1

Given that, A + B $=12+$ B + C
⇒ A - C $=12$
Therefore, C is younger than A by $12$ years

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Solution 2

Total age of A and B is $12$ years more than total age of B and C.

Since B is common in both sides, C is $12$ years younger than A.

29. Sachin's age after $15$ years will be $5$ times his age $5$ years back. Find out the present age of Sachin?
A. $10$ years	B. $11$ years
C. $12$ years	D. $13$ years

answer with explanation

Answer: Option A
Explanation:
Let present age of Sachin $=x.$ Then,

$(x+15)=5(x-5)\Rightarrow 4x=40\Rightarrow x=10$

30. Sandeep's age after six years will be three-seventh of his father's age. Ten years ago the ratio of their ages was $1:5$. What is Sandeep's father's age at present?
A. $30$ years	B. $40$ years
C. $50$ years	D. $60$ years

answer with explanation

Answer: Option C
Explanation:
Let the age of Sandeep and his father before $10$ years be $x$ and $5x$ respectively.

Given that Sandeep's age after six years will be three-seventh of his father's age
$\Rightarrow x+16=\frac{3}{7}(5x+16)\Rightarrow 7x+112=15x+48\Rightarrow 8x=64\Rightarrow x=8$

Sandeep's father's present age
$=5x+10=5\times 8+10=50$