# Problems on ages

1. Raghu’s age after 15 years will be 5 times his age 5 years back. What is the present age of Raghu ?

A. 6 years

B. 8 years

C. 10 years

D. 12 years

Ans: C

Explanation:

$\text&space;{Let&space;Raghu's&space;present&space;age&space;be}&space;\,\,&space;x&space;\,&space;\,&space;\text&space;{years.&space;Then,}$

$\text&space;{Raghu's&space;age&space;after&space;15&space;years}&space;=&space;\left&space;(&space;x&space;+&space;15&space;\right&space;)&space;\text&space;{years.}$

$\text&space;{Raghu's&space;age&space;5&space;years&space;back}&space;=&space;\left&space;(&space;x&space;-&space;5&space;\right&space;)&space;\text&space;{years.}$

$x&space;+&space;15&space;=&space;5\left&space;(&space;x&space;-&space;5&space;\right&space;)$

$x&space;+&space;15&space;=&space;5x&space;-&space;25$

$4x&space;=&space;40$

$x&space;=&space;10$

2. The product of the ages of Ankit and Nikita is 240. If twice the age of Nikita is more than Ankit’s age by 4 years, what is Nikita’s age ?

A. 8 years

B. 10 years

C. 12 years

D. 6 years

Ans: C

Explanation:

$\text&space;{Let&space;Ankit's&space;age&space;be}\,\,&space;x&space;\,\,&space;\text&space;{years.&space;Then,&space;Nikita's&space;age}&space;=&space;\frac{240}{x}&space;\text&space;{years.}$

$2&space;\times&space;\frac{240}{x}&space;-&space;x&space;=&space;4$

$480&space;-&space;x^{2}&space;=&space;4x$

$x^{2}+4x-480&space;=&space;0$

$\left&space;(&space;x&space;+&space;24&space;\right&space;)\left&space;(&space;x&space;-&space;20&space;\right&space;)&space;=&space;0$

$x&space;=&space;20$

$\text{Hence,&space;Nikita's&space;age}&space;=&space;\left&space;(&space;\frac{240}{20}&space;\right&space;)&space;\text{years}&space;=&space;\text&space;{12&space;years}$

3. The present age of a father is 3 years more than three times the age of his son. Three years hence, father’s age will be 10 years more than twice the age of the son. Find the present age of the father ?

A. 28 years

B. 33 years

C. 35 years

D. 29 years

Ans: B

Explanation:

$\text&space;{Let&space;the&space;son's&space;present&space;age&space;be}&space;\,&space;\,&space;x&space;\,\,\text&space;{years.}$

$\text&space;{Then&space;father's&space;present&space;age}&space;=&space;\left&space;(&space;3x&space;+&space;3&space;\right&space;)&space;\text&space;{years.}$

$\left&space;(&space;3x&space;+&space;3&space;+&space;3&space;\right&space;)&space;=&space;2&space;\left&space;(&space;x&space;+&space;3&space;\right&space;)&space;+&space;10$

$3x&space;+&space;6&space;=&space;2x&space;+&space;16$

$x&space;=&space;10$

$\text&space;{Hence&space;father's&space;present&space;age}&space;=&space;\left&space;(&space;3x&space;+&space;3&space;\right&space;)&space;=&space;\left&space;(&space;3&space;\times&space;10&space;+&space;3&space;\right&space;)&space;=&space;\text&space;{33&space;years}$

4. One year ago, the ratio of Gaurav’s and Sachin’s age was 6 : 7 respectively. Four years hence, this ratio would become 7 : 8. How old is Sachin ?

A. 12 years

B. 24 years

C. 36 years

D. 48 years

Ans: C

Explanation:

$\text{Let&space;Gaurav's&space;and&space;Sachin's&space;ages&space;one&space;year&space;ago&space;be}&space;\,\,&space;6x\,\,&space;\text&space;{and}&space;\,\,7x&space;\,\,&space;\text&space;{years&space;respectively.}$

$\text&space;{Gaurav's&space;age&space;4&space;years&space;hence}&space;=&space;\left&space;(&space;6x&space;+&space;1&space;\right&space;)&space;+&space;4&space;=&space;\left&space;(&space;6x&space;+&space;5&space;\right&space;)&space;\text&space;{years}$

$\text{Sachin's&space;age&space;4&space;years&space;hence}&space;=&space;\left&space;(&space;7x&space;+&space;1&space;\right&space;)&space;+&space;4&space;=&space;\left&space;(&space;7x&space;+&space;5&space;\right&space;)&space;\text&space;{years}$

$\frac{6x&space;+&space;5}{7x&space;+&space;5}&space;=&space;\frac{7}{8}$

$8\left&space;(&space;6x&space;+&space;5&space;\right&space;)&space;=&space;7\left&space;(&space;7x&space;+&space;5&space;\right&space;)$

$48x&space;+&space;40&space;=&space;49x&space;+&space;35$

$x&space;=&space;5$

$\text&space;{Hence&space;Sachin's&space;present&space;age}&space;=&space;\left&space;(&space;7x&space;+&space;1&space;\right&space;)&space;=&space;\text&space;{36&space;years}$

5. Suneel’s age after six years will be three-seventh of his father’s age. Ten years ago, the ratio of their ages was 1 : 5. What is Suneel’s father’s age at present ?

A. 25 years

B. 35 years

C. 40 years

D. 50 years

Ans: D

Explanation:

$\text&space;{Let&space;the&space;ages&space;of&space;Suneel&space;and&space;his&space;father&space;10&space;years&space;ago&space;be}&space;\,\,&space;x&space;\,\,&space;\text&space;{and}&space;\,\,5x&space;\,\,&space;\text&space;{years&space;respectively.}$

$\text&space;{Suneel's&space;age&space;after&space;6&space;years}&space;=&space;\left&space;(&space;x&space;+&space;10&space;\right&space;)&space;+&space;6&space;=&space;\left&space;(&space;x&space;+&space;16&space;\right&space;)&space;\text{years}$

$\text{Father's&space;age&space;after&space;6&space;years}&space;=&space;\left&space;(&space;5x&space;+&space;10&space;\right&space;)&space;+&space;6&space;=&space;\left&space;(&space;5x&space;+&space;16&space;\right&space;)&space;\text&space;{years}$

$\left&space;(&space;x&space;+&space;16&space;\right&space;)&space;=&space;\frac{3}{7}\left&space;(&space;5x&space;+&space;16&space;\right&space;)$

$7\left&space;(&space;x&space;+&space;16&space;\right&space;)&space;=&space;3\left&space;(&space;5x&space;+&space;16&space;\right&space;)$

$7x&space;+&space;112&space;=&space;15x&space;+&space;48$

$8x&space;=&space;64$

$x&space;=&space;8$

$\text&space;{Hence,&space;Suneel&space;father's&space;present&space;age}&space;=&space;\left&space;(&space;5x&space;+&space;10&space;\right&space;)&space;=&space;\text&space;{50&space;years.}$

6. Sachin is younger than Rahul by 4 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin ?

A. 16 years

B. 18 years

C. 28 years

D. None of these

Ans: D

Explanation:

$\text&space;{Let&space;Rahul's&space;age&space;be}&space;\,\,&space;x&space;\,\,&space;\text&space;{years.&space;Then,&space;Sachin's&space;age}&space;=&space;\left&space;(&space;x&space;-&space;7&space;\right&space;)&space;\text&space;{years}$

$\frac{x-7}{x}&space;=&space;\frac{7}{9}$

$9x&space;-&space;63&space;=&space;7x$

$2x&space;=&space;63$

$x&space;=&space;31.5$

$\text&space;{Hence,&space;Sachin's&space;age}&space;=&space;\left&space;(&space;x&space;-&space;7&space;\right&space;)&space;=&space;24.5&space;\text&space;{years}$

7. The ratio between the present ages of P and Q is 6 : 7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years ?

A. 3 : 4

B. 3 : 5

C. 4 : 3

D. None of these

Ans: D

Explanation:

$\text&space;{Let&space;P's&space;age&space;and&space;Q's&space;age&space;be}&space;\,\,&space;6x&space;\,\,&space;\text&space;{years&space;and}&space;\,\,&space;7x&space;\,\,&space;\text&space;{years&space;respectively.}$

$\text&space;{Then,}&space;\,\,&space;7x&space;-&space;6x&space;=&space;4$

$x&space;=&space;4$

$\text&space;{Required&space;ratio}&space;=&space;\left&space;(&space;6x&space;+&space;4&space;\right&space;)&space;:&space;\left&space;(&space;7x&space;+&space;4&space;\right&space;)&space;=&space;28&space;:&space;32&space;=&space;7&space;:8$

8. The ratio the present ages of P and Q is 5 : 7 respectively. If the difference between Qs present age and Ps age after 6 years is 2, what is the total of Ps and Qs present ages ?

A. 48 years

B. 52 years

C. 56 years

D. None of these

Ans: A

Explanation:

$\text&space;{Let&space;the&space;present&space;ages&space;of&space;P&space;and&space;Q&space;be}&space;\,\,5x&space;\,\,&space;\text&space;{years&space;and}&space;\,\,&space;7x&space;\,\,&space;\text&space;{years&space;respectively.}$

$\text&space;{Then},&space;7x&space;-&space;\left&space;(&space;5x&space;+&space;6&space;\right&space;)&space;=&space;2$

$2x&space;=&space;8$

$x&space;=&space;4$

$\text&space;{Required&space;sum}&space;=&space;5x&space;+&space;7x&space;=&space;12x&space;=&space;\text&space;{48&space;years&space;}$

9. At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun`s age will be 26 years. What is the age of Deepak at present ?

A. 12 years

B. 15 years

C. 19 years

D. 21 years

Ans: B

Explanation:

$\text&space;{Let&space;the&space;present&space;ages&space;of&space;Arun&space;and&space;Deepak&space;be}&space;\,\,&space;4x&space;\,\,&space;\text&space;{years&space;and}&space;\,\,&space;3x&space;\,\,&space;\text&space;{years&space;respectively.&space;Then,}$

$4x&space;+&space;6&space;=&space;26$

$4x&space;=&space;20$

$x&space;=&space;5$

$\text&space;{Deepak's&space;age}&space;=&space;3x&space;=&space;15&space;\,\,&space;\text&space;{years}$

10. Present ages of X and Y are in the ratio 5 : 6 respectively. Seven years hence this ratio will become 6 : 7 respectively. What is X’s present age in years ?

A. 35

B. 42

C. 49

D. None of these

Ans: A

Explanation:

$\text&space;{Let&space;the&space;present&space;ages&space;of&space;X&space;and&space;Y&space;be&space;}&space;\,\,&space;5x&space;\,\,&space;\text&space;{years&space;and}&space;\,\,&space;6x&space;\,\,&space;\text&space;{years&space;respectively.}$

$\frac{5x+7}{6x+7}&space;=&space;\frac{6}{7}$

$7\left&space;(&space;5x&space;+&space;7&space;\right&space;)&space;=&space;6\left&space;(&space;6x&space;+&space;7&space;\right&space;)$

$x&space;=&space;7$

$\text{X's&space;present&space;age}&space;=&space;5x&space;=&space;35&space;\,\,&space;\text&space;{years.}$