17. The age of Arvind's father is 4 times his age. If 5 years ago, father's age was 7 times the age of his son at the time, what is Arvind's father's present age ?
a. 35 years
b. 40 years
c. 70 years
d. 84 years

Answer: B
Explanation:
Arvind's age (say) $= x$ years
His father's age $= 4x$ years
Ages of aravind and his father 5 years ago $=x-5,\;4x-5$
$\begin{array}{*{20}{|c|cc|}} \hline
{}&{Father}&{Aravind} \\ \hline
\text{5 yeras ago ages}&{4x-5}&{x-5} \\ \hline
\text{Present ages}&{4x}&{x} \\ \hline
\end{array}$
$ \Rightarrow \dfrac{{4x - 5}}{{x - 5}} = \dfrac{7}{1}$
$ \Rightarrow 4x - 5 = 7x - 35$
$ \Rightarrow 3x = 30$
$ \Rightarrow x = 10$
$\therefore $ Arvind's father's age $= 4 \times 10 = 40$ years

18. Pushpa is twice as old as Rita was two years ago. If the difference between their ages is 2 years, how old is Pushpa today ?
a. 6 years
b. 8 years
c. 10 years
d. 12 years
d. None of these

Answer: B
Explanation:
Rita's age 2 years ago (say) $= x$ years
Pushpa's present age $= 2x$ years
$\begin{array}{*{20}{|c|c|c|}} \hline
{}&{Rita}&{Pushpa} \\ \hline
\text{2 yeras ago ages}&{}&\color{red}x \\ \hline
\text{Present ages}&\color{red}{2x}&{x+2} \\ \hline
\end{array}$
$\Rightarrow 2x - (x + 2) = 2 $
$\Rightarrow x = 4$
Pushpa's present age $= 2 \times 4 = 8$ years

19. Five years ago Vinay's age was one-third of the age of Vikas and now Vinay's age is 17 years. What is the present age of Vikas ?
a. 9 years
b. 36 years
c. 41 years
d. 51 years

Answer: C
Explanation:
Let the present age of Vikas be x years
Then, 17-5 = $\displaystyle\frac{1}{3}$(x - 5)
or x - 5 = 36 or x = 41

20. The sum of the ages of a father and son is 45 years. Five years ago the product of their ages was 4 times the father's age at that time. The present ages of the father and son, respectively are,
a. 25 years, 10 years
b. 36 years, 9 years
c. 39 years, 5 years
d. none of these

Answer: B
Explanation:
Let the present ages of father and son be x years and (45-x) years
Then, (x - 5)(45 - x - 5)=4(x - 5)
45 - x - 5 = 4 or x = 36
The present ages of father and son are 36 years and 9 years respectively.

21. Rajan's age is 3 times that of Ashok. In 12 years, Rajan's age will be double the age of Ashok. Rajan's present age is :
a. 27 years
b. 32 years
c. 36 years
d. 40 years

Answer: C
Explanation:
Let Ashok's age be x years
Then, Rajan's age = 3x years
2(x + 12)=(3x + 12) or x = 12
Hence, Rajan's age = 3x years
2(x + 12)=(3x + 12) or x = 12
Hence Rajan's present age is 36 years

22. In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is :
a. 19 years
b. 29 years
c. 39 years
d. 49 years

Answer: C
Explanation:
Let the present ages of B and A be x years and (x+9) years respectively. Then 10 years ago B's age is (x - 10) and in the next 10 years A's age is (x + 19)
Given that A's age is twice of B
So (x + 19) = 2 x (x - 10) $ \Rightarrow $ x + 19 = 2x - 20 $ \Rightarrow $ x = 39

23. Mr.Sohanlal is 4 times as old as his son. Four years hence the sum of their ages will be 43 years. The present age of son is :
a. 5 years
b. 7 years
c. 8 years
d. 10 years

Answer: B
Explanation:
Let the son's age be x years
Then, (x + 4) + (4x + 4) = 43
or 5x = 35 or x = 7

24. The sum of the ages of a son and father is 56 years. After 4 years, the age of the father will be three times that of the son. Their ages respectively are:
a. 12 years, 44 years
b. 16 years, 42 years
c. 16 years, 48 years
d. 18 years, 36 years

Answer: A
Explanation:
Let the present ages of son and father be x years
and (56-x) years respectively.
Then (56 - x + 4)=3(x + 4)
or 4x = 48 or x = 12
So their ages are 12 years, 44 years respectively.

25. The sum of the ages of a mother and daughter is 50 years. Also, 5 years ago, the mother's age was 7 times the age of the daughter. The present ages of the mother and daughter respectively are :
a. 35 years, 15 years
b. 38 years, 12 years
c. 40 years, 10 years
d. 42 years, 8 years

Answer: C
Explanation:
Let the daughter's present age be x years. Then, mother's present age = (50-x) years.
Now, 7(x - 5)=(50 - x - 5) or x = 10
So, their present ages are 40 years and 10 years.