Quant Quiz

Problems on Age - Solved Examples(Set 5)

21. The ages of two persons differ by $16$ years. $6$ years ago, the elder one was $3$ times as old as the younger one. What are their present ages of the elder person?
A. $10$	B. $20$
C. $30$	D. $40$

answer with explanation

Answer: Option C
Explanation:
Let present age of the elder person $=x$ and
present age of the younger person $=x-16$

$(x-6)=3(x-16-6)\Rightarrow x-6=3x-66\Rightarrow 2x=60\Rightarrow x=\frac{60}{2}=30$

22. Present age of a father is $3$ years more than three times the age of his son. Three years hence, father's age will be $10$ years more than twice the age of the son. What is father's present age?
A. $30$ years	B. $31$ years
C. $32$ yeas	D. $33$ years

answer with explanation

Answer: Option D
Explanation:
Let the present age the son $=x$
Then, present age of the father $=3x+3$

Given that, three years hence, father's age will be $10$ years more than twice the age of the son
$\Rightarrow (3x+3+3)=2(x+3)+10\Rightarrow x=10$

Father's present age
$=3x+3=3\times 10+3=33$

23. Kamal was $4$ times as old as his son $8$ years ago. After $8$ years, Kamal will be twice as old as his son. Find out the present age of Kamal.
A. $40$ years	B. $38$ years
C. $42$ years	D. $36$ years

answer with explanation

Answer: Option A
Explanation:
Let age of the son before $8$ years $=x$
Then, age of Kamal before $8$ years ago $=4x$

After $8$ years, Kamal will be twice as old as his son
$\Rightarrow 4x+16=2(x+16)\Rightarrow x=8$

Present age of Kamal
$=4x+8=4\times 8+8=40$

24. If $6$ years are subtracted from the present age of Ajay and the remainder is divided by$18$, then the present age of Rahul is obtained. If Rahul is $2$ years younger to Denis whose age is $5$ years, then what is Ajay's present age?
A. $50$ years	B. $60$ years
C. $55$ years	D. $62$ years

answer with explanation

Answer: Option B
Explanation:
Present age of Denis $=5$ years
Present age of Rahul $=5-2=3$

Let present age of Ajay $=x$
Then, present age of Rahul $=\frac{x-6}{18}$

$\frac{x-6}{18}=3\Rightarrow x-6=3\times 18=54\Rightarrow x=54+6=60$

25. The ratio of the age of a man and his wife is $4:3$. At the time of marriage the ratio was $5:3$ and After $4$ years this ratio will become $9:7$. How many years ago were they married?
A. $8$ years	B. $10$ years
C. $11$ years	D. $12$ years

answer with explanation

Answer: Option D
Explanation:
Let the present age of the man and his wife be $4x$ and $3x$ respectively.

After $4$ years this ratio will become $9:7$
$\Rightarrow (4x+4):(3x+4)=9:7\Rightarrow 7(4x+4)=9(3x+4)\Rightarrow 28x+28=27x+36\Rightarrow x=8$

Present age of the man $=4x=4\times 8=32$
Present age of his wife $=3x=3\times 8=24$

Assume that they got married before $t$ years. Then,
$(32-t):(24-t)=5:3\Rightarrow 3(32-t)=5(24-t)\Rightarrow 96-3t=120-5t\Rightarrow 2t=24\Rightarrow t=\frac{24}{2}=12$