Quantitative

Problems on Age - Solved Examples(Set 4)

16. The present ages of A,B and C are in proportions $4:7:9$. Eight years ago, the sum of their ages was $56$. What are their present ages (in years)?
A. Insufficient data	B. $16,30,40$
C. $16,28,40$	D. $16,28,36$

answer with explanation

Answer: Option D
Explanation:
Solution 1

Let present age of A,B and C be $4x,7x$ and $9x$ respectively.

$(4x-8)+(7x-8)+(9x-8)=56\Rightarrow 20x=80\Rightarrow x=4$

Hence present age of A, B and C are
$4\times 4,7\times 4$ and $9\times 4$ respectively.
i.e., $16,28$ and $36$ respectively.

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Solution 2

Sum of their present ages $=56+3\times 8=80$

Present age of A $=80\times \frac{4}{20}=16$

Present age of B $=80\times \frac{7}{20}=28$

Present age of C $=80\times \frac{9}{20}=36$

17. A person's present age is two-fifth of the age of his mother. After $8$ years, he will be one-half of the age of his mother. What is the present age of the mother?
A. $60$	B. $50$
C. $40$	D. $30$

answer with explanation

Answer: Option C
Explanation:
Solution 1

Let present age of the person $=x$
Then, present age of the mother $=\frac{5x}{2}$

Given that, after $8$ years, the person will be one-half of the age of his mother.
$\Rightarrow (x+8)=\frac{1}{2}(\frac{5x}{2}+8)\Rightarrow 2x+16=\frac{5x}{2}+8\Rightarrow \frac{x}{2}=8\Rightarrow x=16$

Present age of the mother
$=\frac{5x}{2}=\frac{5\times 16}{2}=40$

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Solution 2

Let present age of the mother $=5x$
Then, present age of the person $=2x$

$5x+8=2(2x+8)5x+8=4x+16x=8$present age of the mother $=5x=40$

18. A is as much younger than B and he is older than C. If the sum of the ages of B and C is$50$ years, what is definitely the difference between B and A's age?
A. Data inadequate	B. $3$ years
C. $2$ years	D. $5$ years

answer with explanation

Answer: Option A
Explanation:
Age of C $<$ Age of A $<$ Age of B

Given that sum of the ages of B and C is $50$ years.

Now we need to find out (B's age - A's age). But this cannot be determined with the given data.

19. Sobha's father was $38$ years of age when she was born while her mother was $36$ years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
A. $6$ years	B. $5$ years
C. $4$ years	D. $3$ years

answer with explanation

Answer: Option A
Explanation:
Solution 1

Let Sobha's age $=x$ and
her brother's age $=x-4$

Sobha's father's age $=x+38$
Sobha's mother's age $=(x-4)+36=x+32$

Sobha's father's age - Sobha's mother's age
$=(x+38)-(x+32)=6$

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Solution 2

Age of Sobha's father when Sobha was born $=38$

Age of Sobha's mother when Sobha was born $=36-4=32$

Required difference of age $=38-32=6$

20. The age of father $10$ years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. What is the ratio of their present ages?
A. $7:3$	B. $3:7$
C. $9:4$	D. $4:9$

answer with explanation

Answer: Option A
Explanation:
Let age of the son before $10$ years $=x$ and
age of the father before $10$ years $=3x$

$(3x+20)=2(x+20)\Rightarrow x=20$

Age of the son at present $=x+10=20+10=30$
Age of the father at present $=3x+10=3\times 20+10=70$

Required ratio $=70:30=7:3$