## Age Problems

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

A. 8 years

B. 10 years

C. 12 years

D. 6 years

Explanation:


Let Raghu's present age be $x$ years. Then,

Raghu's age after 15 years = ($x$ + 15)  years.

Raghu's age 5 years back = ($x$ – 5)  years.

($x$+ 15) = 5($x$ – 5)

$x$ + 15 = 5$x$ – 25

4$x$ = 40

$x$ = 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

Explanation:

			Let Ankit's age be $x$ years. Then, Nikita's age = $\frac{240}{x}$ years.
$2 \times \frac{240}{x} - x = 4$
$480 - x^2 = 4x$
$x^2 + 4x - 480 = 0$
$\left(x\ +\ 24\right) \left(x-20\right) = 0$
$x$ = 20
Hence, Nikita's age = $\left(\frac{240}{20}\right)$ years = 12 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. 8 years

B. 10 years

C. 12 years

D. 6 years

Explanation:

			Let the son's present age be $x$ years.
Then father's present age = $\left(3x+3\right)$ years.
$\left(3x + 3 + 3\right) = 2\left(x+3\right) + 10$
$3x + 6 = 2x + 16$
$x = 10$
Hence father's present age = $\left(3x+3\right)$ = $\left(3\times 10+3\right)$ = 33 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. 8 years

B. 10 years

C. 12 years

D. 6 years

Explanation:

			Let Gaurav's and Sachin's ages one year ago be 6$x$ and 7$x$ years

respectively.

Gaurav's age 4 years hence = $(6x+1)$ + 4 = $(6x+5)$ years

Sachin's age 4 years hence = $(7x+1)$ + 4 = $(7x+5)$ years

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

8$(6x+5)$ $=$ 7$(7x+5)$

48$x$ + 40 = 49$x$ + 35

$x$ = 5

Hence Sachins present age = $(7x+1)$ = 36 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 father's age at present ?

A. 8 years

B. 10 years

C. 12 years

D. 6 years

Explanation:

			Let the ages of Suneel and his father 10 years ago be $x$ and 5$x$ years respectively.

Suneel's age after 6 years = $(x+10)$ + 6 = $(x+16)$ years

Father's age after 6 years = $(5x+10)$ + 6 = $(5x+16)$ years

$(x + 16)$ = $\frac{3}{7}(5x + 16)$

7$(x + 16)$ = 3$(5x + 16)$

7$x$ + 112 = 15$x$ + 48

8$x$ = 64

$x$= 8

Hence, Suneel father's present age = $(5x+10)$ = 50 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. 8 years

B. 10 years

C. 12 years

D. 6 years

Explanation:

			Let Rahul's age be $x$ years. Then, Sachin's age = $(x -7)$ years

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

9$x$ - 63 = 7$x$

2$x$ = 63

$x$ = 31.5

Hence, Sachin's age = $(x -7)$ = 24.5 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. 8 years

B. 10 years

C. 12 years

D. 6 years

			Let P's age and Q's age be 6$x$ years and 7$x$ years respectively.
Then, 7$x$ - 6$x$ = 4
$x$ = 4
Required ratio = $(6x+4)$ : $(7x+4)$ = 28 : 32 = 7 : 8			`