Quant Quiz

Problems on Age - Solved Examples(Set 2)

6. The sum of ages of $5$ children born at the intervals of $3$ years each is $50$ years. Find out the age of the youngest child?
A. $6$ years	B. $5$ years
C. $4$ years	D. $3$ years

answer with explanation

Answer: Option C
Explanation:
Let the age of the youngest child $=x$

Then, the ages of $5$ children can be written as $x,(x+3),(x+6),(x+9)$ and $(x+12)$

$x+(x+3)+(x+6)+(x+9)$ $+(x+12)=50$
$\Rightarrow 5x+30=50\Rightarrow 5x=20\Rightarrow x=\frac{20}{5}=4$

7. A is two years older than B who is twice as old as C. The total of the ages of A, B and C is$27$. How old is B?
A. $10$	B. $9$
C. $8$	D. $7$

answer with explanation

Answer: Option A
Explanation:
Let age of C $=x$. Then,
Age of B $=2x$
Age of A $=2+2x$

Total age of A,B and C $=27$
$\Rightarrow (2+2x)+2x+x=27\Rightarrow 5x=25\Rightarrow x=\frac{25}{5}=5$

B's age $=2x=2\times 5=10$

8. The average age of a class of $22$ students is $21$ years. The average increased by $1$ when the teacher's age also included. What is the age of the teacher?
A. $48$	B. $45$
C. $43$	D. $44$

answer with explanation

Answer: Option D
Explanation:
Solution 1

Total age of all students $=22\times 21$

Total age of all students + Age of the teacher $=23\times 22$

Age of the teacher
$=23\times 22-22\times 21=22(23-21)=22\times 2=44$

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Solution 2

If age of the teacher was $21$, average would not have changed.

Since average increased by $1$,
Age of the teacher $=21+23\times 1=44$

9. A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is $38$ years now, what was the son's age five years back?
A. $20$ years	B. $18$ years
C. $14$ years	D. $22$ years

answer with explanation

Answer: Option C
Explanation:
Let son's present age be $x$ years. Then,

$(38-x)=x\Rightarrow 2x=38\Rightarrow x=\frac{38}{2}=19$

Son's age $5$ years back =$19-5=14$

10. Ayisha's age is $1/6\text{th}$ of her father's age. Ayisha's father's age will be twice Shankar's age after $10$ years. If Shankar's eight birthdays was celebrated two years before, then what is Ayisha's present age.
A. $10$ years	B. $12$ years
C. $8$ years	D. $5$ years

answer with explanation

Answer: Option D
Explanation:
Solution 1

Let Ayisha's present age $=x$
Then, her father's age $=6x$

Given that Ayisha's father's age will be twice Shankar's age after $10$ years.
Therefore, Shankar's age after $10$ years $=\frac{1}{2}(6x+10)=3x+5$

Also given that Shankar's eight birthdays was celebrated two years before.
Therefore, Shankar's age after $10$ years $=8+12=20$

$3x+5=20\Rightarrow x=\frac{15}{3}=5$

Therefore, Ayisha's present age $=5$ years

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Solution 2

Shankar's present age $=8+2=10$

Ayisha's father's age after $10$ years $=2(10+10)=40$
Ayisha's father's present age $=40-10=30$

Ayisha's present age $=\frac{1}{6}\times 30=5$