Working methodology: In these problems, two persons initial ages will be given. and before or after several years, their ratio of the ages will be given. Multiply the ratio of their initial age by x or some variable and take them as their initial age. Now if final ratio has been given, equate this ratio with that ratio and find x. Or proceed according to the problem.

1. The present age of Gopal is 15 years. His age after 7 years is
a. 20
b. 21
c. 22
d. 23

Answer: C

Explanation:
Gopal's age after after 7 years = $15 + 7 = 22$

2. The age of Jaya 5 years ago is 12 years. 3 years hence her age is
a. 20
b. 21
c. 22
d. 23
d. None of these

Answer: D

Explanation:
$\begin{array}{*{20}{|c|cc|}} \hline
{}&{Jaya's\; age} \\ \hline
\text{5 yeras ago}&{12} \\ \hline
\text{Present age}&{17} \\ \hline
\text{3 years hence}&{20} \\ \hline
\end{array}$
The age of Jaya 5 years ago = $12$ years
Current age of Jaya = $12 + 5 = 17$ years
Jaya's age 3 years hence = $17 + 3 = 20$ years

3. The difference between the ages of Latha and her father 7 years ago is 25 years. The difference between their ages after 10 years is :
a. 20 years
b. 25 years
c. 35 years
d. 45 years

Answer: B

Explanation:
The difference between two person's age doesn't change with progress of years. It is constant. So answer is $25$ years.

4. The ratio of the ages of Meena and Meera is 4:3. The sum of their ages is 28 years. The ratio of their ages after 8 years will be :
a. 4 : 3
b. 12 : 11
c. 7 : 4
d. 6 : 5

Answer: B

Explanation:
Let Meena's age = $4x$ or Meera's age = $3x$. Then,
$4x + 3x = 28$ $\Rightarrow x = 4$
Meena's age = $4 \times 4 = 16$ years
Meera's age = $4 \times 3 = 12$ years
After 8 years their ages $= 16 + 8 = 24$ and $12 + 8 = 20$.
So ratio = $24 : 20$ = $6 : 5$

5. The ages of Ravi and Rani are in the ratio of 3:5. After 9 years, the ratio of their ages will become 3:4. The present age of Rani is : (in years )
a. 9
b. 15
c. 18
d. 24

Answer: B

Explanation:
Let Ravi's age = $3x$ or Rani's age = $5x$
Their ages after 9 years = $3x+9$, $5x+9$
Given that, the ratio of their ages $= 3 : 4$
$\displaystyle\frac{{3x + 9}}{{5x + 9}} = \displaystyle\frac{3}{4} \Rightarrow 4(3x + 9) = 3(5x + 9) \Rightarrow x = 3$
Rani's age = $15$ years

6. The ratio of the ages of Jaya and Ravi is 2:5. After 8 years, their ages will be in the ratio of 1:2. The difference in their present ages is : ( in years )
a. 24
b. 26
c. 29
d. 32

Answer: A

Explanation:
Let Jaya's age = $2x$ or Ravi's age = $5x$.
Their ages after 8 years = $2x+8$, $5x+8$
Given that, the ratio of their ages = 1 : 2
$\therefore \displaystyle\frac{{2x + 8}}{{5x + 8}} = \displaystyle\frac{1}{2}$
$\Rightarrow 2(2x + 8)= (5x+8)$
$\Rightarrow x = 8$
Jaya's age = $2 \times 8 = 16$ years
Ravi's age = $5 \times 8 = 40$ years
Difference between their ages = $24$ years

7. Ten years ago A was half of B in age. If the ratio of their present ages is 3:4 , what will be the total of their present ages ?
a. 8 years
b. 20 years
c. 35 years
d. 45 years

Answer: C

Explanation:
Let Then B's age 10 years ago = $2x$ years
A's age 10 years ago = $x$ years
Their present ages = $x + 10$, $2x + 10$
$\begin{array}{*{20}{|c|cc|}} \hline
{}&{A}&{B} \\ \hline
\text{10 years ago ages}&{x}&{2x} \\ \hline
\text{Present ages}&{x+10}&{2x+10} \\ \hline
\end{array}$
$\displaystyle\frac{{x + 10}}{{2x + 10}} = \displaystyle\frac{3}{4}$
$\Rightarrow 4(x + 10) = 3(2x + 10)$
$\Rightarrow x = 5$
Total of heir present ages = $(x + 10 + 2x + 10)$ = $(3x + 20) = 35$ years

8. The ratio of Vimal's age and Aruna's age is 3:5 and sum of their ages is 80 years. The ratio of their ages after 10 years will be :
a. 2 : 3
b. 1 : 2
c. 3 : 2
d. 3 : 5

Answer: B

Explanation:
Let the ages of Vimal and Aruna = $3x, 5x$
$\therefore 3x + 5x = 80$
$\Rightarrow x = 10$
Ratio of their ages after 10 years = $(3x + 10 : 5x + 10)$ $= (3 \times 10 + 10 : 5 \times 10 + 10)$ $= 40 : 60 = 2 : 3$