Quant Quiz

Problems on Age - Solved Examples(Set 3)

11. The sum of the present ages of a son and his father is $60$ years. Six years ago, father's age was five times the age of the son. After $6$ years, what will be son's age?
A. $23$ years	B. $22$ years
C. $21$ years	D. $20$ years

answer with explanation

Answer: Option D
Explanation:
Let the present age of the son $=x$
Then, present age of the father $=(60-x)$

Six years ago father's age was $5$ times the age of the son
$\Rightarrow (60-x)-6=5(x-6)\Rightarrow 84=6x\Rightarrow x=\frac{84}{6}=14$

Son's age after $6$ years
$=x+6=14+6=20$

12. Kiran is younger than Bineesh by $7$ years and their ages are in the respective ratio of $7:9.$ How old is Kiran?
A. $25$	B. 24.5
C. $24$	D. $23.5$

answer with explanation

Answer: Option B
Explanation:
Solution 1

Let age of Kiran and Bineesh be $7x$ and $9x$ respectively

$7x=9x-7x=\frac{7}{2}=3.5$

Kiran's age $=7x=7\times 3.5=24.5$

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Solution 2

Kiran's age : Bineesh's age $=7:9$

$9-7=2$
$2$ units $=7$(∵ difference in age is $7$)
$\Rightarrow 7$ units $=\frac{7\times 7}{2}=24.5$

i.e., Kiran's age $=24.5$

13. Six years ago, the ratio of the ages of Vimal and Saroj was $6:5$. Four years hence, the ratio of their ages will be $11:10$. What is Saroj's age at present?
A. $18$	B. $17$
C. $16$	D. $15$

answer with explanation

Answer: Option C
Explanation:
Given that, six years ago, the ratio of the ages of Vimal and Saroj $=6:5$

Hence we can assume that
age of Vimal six years ago $=6x$
age of Saroj six years ago $=5x$

After $4$ years, the ratio of their ages $=11:10$
$\Rightarrow (6x+10):(5x+10)=11:10\Rightarrow 10(6x+10)=11(5x+10)\Rightarrow 5x=10\Rightarrow x=\frac{10}{5}=2$

Saroj's present age
$=(5x+6)=5\times 2+6=16$

14. At present, the ratio between the ages of Shekhar and Shobha is $4:3$. After $6$ years, Shekhar's age will be $26$ years. Find out the age of Shobha at present?
A. $15$ years	B. $14$ years
C. $13$ years	D. $12$ years

answer with explanation

Answer: Option A
Explanation:
After $6$ years, Shekhar's age will be $26$ years
Therefore, Present age of Shekhar $=26-6=20$

Let present age of Shobha $=x$

Then,
$\frac{20}{x}=\frac{4}{3}x=\frac{20\times 3}{4}=15$

15. My brother is $3$ years elder to me. My father was $28$ years of age when my sister was born while my mother was $26$ years of age when I was born. If my sister was $4$ years of age when my brother was born, then what was the age of my father when my brother was born?
A. $35$ years	B. $34$ years
C. $33$ years	D. $32$ years

answer with explanation

Answer: Option D
Explanation:
Solution 1

Let my age $=x$

Then
My brother's age $=x+3$
My mother's age $=x+26$
My sister's age $=(x+3)+4=x+7$
My father's age $=(x+7)+28=x+35$

Age of my father when my brother was born
$=x+35-(x+3)=32$

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Solution 2

Father's age was $28$ years when my sister was born.

My sister's age was $4$ years when my brother was born.

Therefore, father's age was $28+4=32$ years when my brother was born
.