Quant Quiz

Problems on Age - Solved Examples(Set 1)

1. Ten years ago, P was half of Q's age. If the ratio of their present ages is $3:4$, what will be the total of their present ages?
A. $45$	B. $40$
C. $35$	D. $30$

answer with explanation

Answer: Option C
Explanation:
Let present age of P and Q be $3x$ and $4x$ respectively.

Ten years ago, P was half of Q's age
$\Rightarrow (3x-10)=\frac{1}{2}(4x-10)\Rightarrow 6x-20=4x-10\Rightarrow 2x=10\Rightarrow x=5$

Total of their present ages
$=3x+4x=7x=7\times 5=35$

2. Father is aged three times more than his son Sunil. After $8$ years, he would be two and a half times of Sunil's age. After further $8$ years, how many times would he be of Sunil's age?
A. $4$ times	B. $5$ times
C. $2$ times	D. $3$ times

answer with explanation

Answer: Option C
Explanation:
Assume that Sunil's present age $=x$.
Then, father's present age $=3x+x=4x$

After $8$ years, father's age $=2\frac{1}{2}$ times of Sunils' age
$\Rightarrow (4x+8)=2\frac{1}{2}(x+8)\Rightarrow 4x+8=\frac{5}{2}(x+8)\Rightarrow 8x+16=5x+40\Rightarrow 3x=40-16=24\Rightarrow x=\frac{24}{3}=8$

After further $8$ years,
Sunil's age $=x+8+8=8+8+8=24$
Father's age $=4x+8+8=4\times 8+8+8=48$

Father's age/Sunil's age $=\frac{48}{24}=2$

3. A man's age is $125\%$ of what it was $10$ years ago, but $83\frac{1}{3}\%$ of what it will be after $10$years. What is his present age?
A. $70$	B. $60$
C. $50$	D. $40$

answer with explanation

Answer: Option C
Explanation:
Let the age before $10$ years $=x$. Then,

$\frac{125x}{100}=x+10\Rightarrow 125x=100x+1000\Rightarrow x=\frac{1000}{25}=40$

Present age $=x+10=40+10=50$

4. A man is $24$ years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
A. $23$ years	B. $22$ years
C. $21$ years	D. $20$ years

answer with explanation

Answer: Option B
Explanation:
Let present age of the son $=x$ years
Then, present age the man $=(x+24)$ years

Given that, in $2$ years, man's age will be twice the age of his son
$\Rightarrow (x+24)+2=2(x+2)\Rightarrow x=22$

5. Present ages of Kiran and Syam are in the ratio of $5:4$ respectively. Three years hence, the ratio of their ages will become $11:9$ respectively. What is Syam's present age in years?
A. $28$	B. $27$
C. $26$	D. $24$

answer with explanation

Answer: Option D
Explanation:
Ratio of the present age of Kiran and Syam $=5:4$

Let present age of Kiran $=5x$
Present age of Syam $=4x$

After $3$ years, ratio of their ages $=11:9$
$\Rightarrow (5x+3):(4x+3)=11:9\Rightarrow 9(5x+3)=11(4x+3)\Rightarrow 45x+27=44x+33\Rightarrow x=33-27=6$

Syam's present age $=4x=4\times 6=24$