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21. The present age of Mr. Sanyal is three times the age of his son. Six years hence , the ratio of their ages will be 5 : 2. What is the present age of Mr. Sanyal ?

A. 48 years

B. 50 years

C. 54 years

D. 60 years

Discuss

Solution:

Let the son's age be

x

years ,
Then Mr. Sanyal's age = 3

x

years

\begin{aligned} ∴ \frac{3 x + 6}{x + 6} = \frac{5}{2} \\ \Rightarrow 2 (3 x + 6) = 5 (x + 6) \\ \Rightarrow 6 x + 12 = 5 x + 30 \\ \Rightarrow x = 18 \end{aligned}

∴ Present age of Mr. Sanyal = 3x years
= (3 × 18) years
= 54 years

22. The average of the ages of a man and his daughter is 34 years. If the respective ratio of their ages four years from now is 14 : 5,what is daughter's present age ?

A. 10 years

B. 12 years

C. 18 years

D. Cannot be determined

Discuss

Solution:

Average age of man and his daughter = 34 years
Their total age = (34 × 2) years = 68 years
Let man's age be x years,
Then daughter age = (68 - x) years

\begin{aligned} ∴ \frac{x + 4}{68 - x + 4} = \frac{14}{5} \\ \Rightarrow 5 (x + 4) = 14 (72 - x) \\ \Rightarrow 5 x + 20 = 1008 - 14 x \\ \Rightarrow 19 x = 988 \\ \Rightarrow x = 52 \end{aligned}

∴ Daughter's present age
= (68 - 52) years
= 16 years

Alternate Solution :
According to question,
After 4 years, the total age of man & daughter is
= [(34 × 2) + 4 + 4]
= 76 years
After 4 years their age ratio is 14 : 5 (given)
So, 4 years after the daughter age will be
= 76 ×

\frac{5}{19}

= 20 years
∴ Daughter present age
= 20 - 4
= 16 years

23. The age of a father 10 years ago was thrice the age of his son. 10 years hence , the father's age will be twice that of his son. The ratio of their present age is = ?

A. 8 : 5

B. 7 : 3

C. 9 : 5

D. 5 : 2

Discuss

Solution:

Let son's age 10 years ago be

x

years
Then, father age 10 years ago = 3

x

years
Son's age now = (

x

+ 10) years,
Father age now = (3

x

+ 10) years

\begin{aligned} (3 x + 10) + 10 = 2 [(x + 10) + 10] \\ \Rightarrow 3 x + 20 = 2 (x + 20) \\ \Rightarrow 3 x + 20 = 2 x + 40 \\ \Rightarrow x = 20 \end{aligned}

Ratio of present ages of father and son

\begin{aligned} = \frac{3 x + 10}{x + 10} \\ = \frac{3 \times 20 + 10}{20 + 10} \\ = \frac{70}{30} \\ = \frac{7}{3} \\ = 7 : 3 \end{aligned}

24. At present Suresh's age is twice the age of his daughter. After 6 year from now, the ratio of the ages of Suresh and his daughter will be 23 : 13. What is the present age of Suresh ?

A. 36 years

B. 40 years

C. 46 years

D. Cannot be determined

Discuss

Solution:

Let daughter's age be x years.
Suresh's age = 2x years

\begin{aligned} ∴ \frac{2 x + 6}{x + 6} = \frac{23}{13} \\ \Rightarrow 13 (2 x + 6) = 23 (x + 6) \\ \Rightarrow 26 x + 78 = 23 x + 138 \\ \Rightarrow 3 x = 60 \\ \Rightarrow x = 20 \end{aligned}

Present age of Suresh = 2x years

\begin{aligned} = (2 \times 20) years \\ =  40 years \end{aligned}

25. Ten years ago, a man was seven times as old as his son. Two years hence, twice his age will be equal to five times the age of his son. What is the present age of the son ?

A. 12 years

B. 13 years

C. 14 years

D. 15 years

Discuss

Solution:

Let son's age 10 years ago be x years.
Then, man's age 10 years ago = 7x years
Son's present age = (x + 10) years,
Man's present age = (7x + 10) years

\begin{aligned} ∴ 2 [(7 x + 10) + 2] = 5 [(x + 10) + 2] \\ \Rightarrow 2 (7 x + 12) = 5 (x + 12) \\ \Rightarrow 14 x + 24 = 5 x + 60 \\ \Rightarrow 9 x = 36 \\ \Rightarrow x = 4 \end{aligned}

Son's present age = (x + 10) years
= (4 + 10) years
= 14 years

26. The ages of Samina and Suhana are in the ratio of 7 : 3 respectively. After 6 years, the ratio of their ages will be 5 : 3. What is the difference in their ages?

A. 6 years

B. 8 years

C. 10 years

D. 12 years

Discuss

Solution:

Let Samina's age be 7x years.
Then, Suhana's age = 3x years

\begin{aligned} ∴ \frac{7 x + 6}{3 x + 6} = \frac{5}{3} \\ \Rightarrow 3 (7 x + 6) = 5 (3 x + 6) \\ \Rightarrow 21 x + 18 = 15 x + 30 \\ \Rightarrow 6 x + 12 \\ \Rightarrow x = 2 \end{aligned}

Difference in their ages = (7x - 3x) years
= 4x years
= (4 × 2) years
= 8 years

27. The ages of A and B are presently in the ratio of 5 : 6 respectively. Six years hence, this ratio became 6 : 7 respectively. What was B's age 5 years ago ?

A. 25 years

B. 30 years

C. 31 years

D. 36 years

Discuss

Solution:

Let A's age be 5x years.
Then, B's age = 6x years

\begin{aligned} ∴ \frac{5 x + 6}{6 x + 6} = \frac{6}{7} \\ \Rightarrow 7 (5 x + 6) = 6 (6 x + 6) \\ \Rightarrow 35 x + 42 = 36 x + 36 \\ \Rightarrow x = 6 \end{aligned}

B's age 5 years ago = (6x - 5) years
= (6 × 6 - 5) years
= 31 years

28. The sum of the ages of a daughter and her mother is 56 years. After 4 years, the age of the mother will be three times that of the daughter. At present their ages are ?

A. 10 years, 46 years

B. 12 years, 44 years

C. 11 years, 45 years

D. 13 years, 43 years

Discuss

Solution:

Let daughter's age be

x

years.
Then, mother's age = (56

- x

) years

\begin{aligned} (56 - x) + 4 = 3 (x + 4) \\ \Rightarrow 60 - x = 3 x + 12 \\ \Rightarrow 4 x = 48 \\ \Rightarrow x = 12 \end{aligned}

∴ Daughter's age = 12 years
And the mother's age = (56

-

12) = 44 years

29. The present age of son is half of the present age of his mother. Ten years ago, his mother's age was thrice the age of her son. What is the present age of the son ?

A. 20 years

B. 25 years

C. 30 years

D. 40 years

Discuss

Solution:

Let mother's age be 2x years,
Then, son's age = x years

\begin{aligned} ∴ (2 x - 10) = 3 (x - 10) \\ \Rightarrow 2 x - 10 = 3 x - 30 \\ \Rightarrow x = 20 \end{aligned}

Son's age = 20 years

30. Ram's son's age is $\frac{1}{3}$ of Ram's wife's age. Ram's wife's age is $\frac{4}{5}$ of Ram's age and Ram's age is $\frac{3}{5}$ of Ram's father's age. Find the age of Ram's son, if Ram's father is 50 years old ?

A. 6 years

B. 8 years

C. 10 years

D. 12 years

Discuss

Solution:

\begin{aligned} Ram's father's age \\ =  50 years, \\ Ram's age \\ = (\frac{3}{5} \times 50) years \\ =  30 years \\ Ram's wife's age \\ = (\frac{4}{5} \times 30) years \\ =  24 years \\ Ram's son's age \\ = (\frac{1}{3} \times 24) years \\ =  8 years \end{aligned}

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