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Home > Practice > Arithmetic Aptitude > Problem on Ages > Miscellaneous

11. The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

A. 8, 20, 28

B. 16, 28, 36

C. 20, 35, 45

D. None of these

Discuss

Solution:

Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
⇒ 20x = 80
⇒ x = 4
∴ Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.

12. Ayesha'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. 2 years

B. 4 years

C. 6 years

D. 8 years

Discuss

Solution:

Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 4) years = 42 years.
∴ Required difference = (42 - 36) years = 6 years.

13. 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. How old is the mother at present?

A. 32 years

B. 36 years

C. 40 years

D. 48 years

Discuss

Solution:

\begin{aligned} Let the mother's present age be x years . \\ Then, the person's present age \\ = \frac{2}{5} x years \\ ∴ \frac{2}{5} x + 8 = \frac{1}{2} (x + 8) \\ \Rightarrow 2 (2 x + 40) = 5 (x + 8) \\ \Rightarrow x = 40 \end{aligned}

14. Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?

A. 1 year

B. 2 years

C. 25 years

D. Data inadequate

Discuss

Solution:

Given that:
1. The difference of age b/w R and Q = The difference of age b/w Q and T.
2. Sum of age of R and T is 50 i.e. (R + T) = 50.

Question: R - Q = ?.
Explanation:
R - Q = Q - T
(R + T) = 2Q
Now given that, (R + T) = 50
So, 50 = 2Q and therefore Q = 25.
Question is (R - Q) = ?
Here we know the value(age) of Q (25), but we don't know the age of R.
Therefore, (R-Q) cannot be determined.

15. 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. The ratio of their present ages is:

A. 5 : 2

B. 7 : 3

C. 9 : 2

D. 13 : 4

Discuss

Solution:

Let the ages of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
⇒ 3x + 20 = 2x + 40
⇒ x = 20
∴ Required ratio
= (3x + 10) : (x + 10)
= 70 : 30
= 7 : 3

16. The ages of Nitish and Vinnee are in the ratio 6 : 5 respectively. After 9 years the ratio of their ages will be 9 : 8. What is the difference in their ages now ?

A. 3 Years

B. 5 Years

C. 7 Years

D. 9 Years

Discuss

Solution:

Let Nishi's age be 6x years,
Then Vinnee's age = 5x years

\begin{aligned} ∴ \frac{6 x + 9}{5 x + 9} = \frac{9}{8} \\ \Rightarrow 8 (6 x + 9) = 9 (5 x + 9) \\ \Rightarrow 48 x - 45 x = 81 - 72 \\ \Rightarrow 3 x = 9 \\ \Rightarrow x = 3 \\ Difference in their ages \\ = (6 x - 5 x) \\ = x years \\ = 3 years \end{aligned}

17. The ages of Shakti and Kanti are in the ratio of 8 : 7 respectively. After 10 years, the ratio of their ages will be 13 : 12. What is the difference between their ages ?

A. 2 Years

B. 4 Years

C. 8 Years

D. 6 Years

Discuss

Solution:

Let Shakti's age be 8

x

years,
Then Kanti's age = 7

x

years

\begin{aligned} ∴ \frac{8 x + 10}{7 x + 10} = \frac{13}{12} \\ \Rightarrow 12 (8 x + 10) = 13 (7 x + 10) \\ \Rightarrow 96 x + 120 = 91 x + 130 \\ \Rightarrow 5 x = 10 \\ \Rightarrow x = 2 \end{aligned}

Difference between their ages

\begin{aligned} = (8 x - 7 x) \\ = x years \\ =  2 years \end{aligned}

18. The ages of A and B are in the ratio 6 : 5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years ?

A. 7 : 6

B. 8 : 7

C. 9 : 8

D. 3 : 4

Discuss

Solution:

\begin{aligned} A's age  = (44 \times \frac{6}{11}) years \\ =  24 years \\ And B's age  = (44 - 24) years \\ =  20 years \end{aligned}

Ratio of their ages after 8 years

\begin{aligned} = \frac{(24 + 8)}{(20 + 8)} \\ = \frac{32}{28} \\ = \frac{8}{7} \\ = 8 : 7 \end{aligned}

19. Farah got married 8 years ago, Today her age is $1 \frac{2}{7}$ times her age at the time of her marriage. At present her daughter's age is one-sixth of her age. What was her daughter's age 3 years ago ?

A. 4 Years

B. 3 Years

C. 6 Years

D. Cannot be determind

Discuss

Solution:

Let Farah's age 8 years ago be x years.
Then , her present age = (x + 8)

\begin{aligned} ∴ x + 8 = \frac{9}{7} x \\ \Rightarrow 7 x + 56 = 9 x \\ \Rightarrow 2 x = 56 \\ \Rightarrow x = 28 \end{aligned}

∴ Farah's age now
= (x + 8) years
= (28 + 8) years
= 36
Her daughter's age now
=

(\frac{1}{6} \times 36)

years
= 6 years
Her daughter's age 3 years ago
= (6 - 3) years
= 3 years

20. The age of a mother today is thrice that of her daughter. After 12 years , the age of the mother will be twice that of her daughter. The present age of the daughter is = ?

A. 12 Years

B. 14 Years

C. 16 Years

D. 18 Years

Discuss

Solution:

Let the daughter's age be x years.
Then, mother age = 3x years
3x + 12 = 2 (x + 12)
⇒ 3x + 12 = 2x + 24
⇒ x = 12
Present age of daughter = 12 years

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