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41. 6 years ago , the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present ?

A. 16 years

B. 18 years

C. 20 years

D. Cannot be determined

Discuss

Solution:

Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years
Then,

\begin{aligned} \frac{(6 x + 6) + 4}{(5 x + 6) + 4} = \frac{11}{10} \\ \Rightarrow \frac{6 x + 10}{5 x + 10} = \frac{11}{10} \\ \Rightarrow 10 (6 x + 10) = 11 (5 x + 10) \\ \Rightarrow 60 x + 100 = 55 x + 100 \\ \Rightarrow 5 x = 10 \\ \Rightarrow x = 2 \end{aligned}

Sagar's present age
= (5x + 6) years
= (5 × 2 + 6) years
= 16 years

42. Sneh's age is $\frac{1}{6}$ th of her father's age. Sneh's father's age will be twice of Vimal's age after 10 years. If Vimal's 8th birthday was celebrated 2 years ago,then what is Sneh's present age ?

A. $6 \frac{2}{3}$ years

B. 10 years

C. 12 years

D. 15 years

Discuss

Solution:

Vimal's present age
= (8 + 2) years
= 10 years
Sneh's father's age
= 2(10 + 10) years
= 40 years
Sneh's age

\begin{aligned} = (\frac{1}{6} \times 40) years \\ = \frac{20}{3} years \\ =  6 \frac{2}{3} years \end{aligned}

43. The ages of Sulekha and Arunima are in the ratio 9 : 8 respectively. After 5 years, the ratio of their ages will be 10 : 9. What is the difference in their ages ?

A. 4 years

B. 5 years

C. 6 years

D. 7 years

Discuss

Solution:

Let Sulekha age be 9 year,
Then Arunima's age = 8x years

\begin{aligned} \frac{9 x + 5}{8 x + 5} = \frac{10}{9} \\ \Rightarrow 9 (9 x + 5) = 10 (8 x + 5) \\ \Rightarrow 81 x + 45 = 80 x + 50 \\ \Rightarrow x = 5 \end{aligned}

Difference in their ages
= (9x - 8x) years
= x years
= 5 years

44. X's age 3 years ago was three times the present age of Y. At present Z's age is twice the age of Y. Also Z is 12 years younger than X. What is the present age of Z ?

A. 15 years

B. 24 years

C. 12 years

D. 18 years

Discuss

Solution:

Let the present age of Y be a years
Three years ago X's age = 3a years
Then, present age of X is (3a + 3)
Z's present age = 2a
According to question
Now, (3a + 3) - 2a = 12
a = 9 year
∴ Present age of Z = 2a = 2 × 9 = 18 years

45. Eight year ago, Poorvi's age was equal to the sum of the present ages of her one son and one daughter. Five years hence, the respective ratio between the ages of her daughter and her son that time will be 7 : 6. If Poorvi's husband is 7 years elder to her and his present age is three times the present age of their son, what is the present age of the daughter ? (in year)

A. 15 years

B. 23 years

C. 19 years

D. 27 years

Discuss

Solution:

Let the age of the son and the daughter of Poorvi be 6a years and 7a years respectively.
5 years hence, present age of son = 6a - 5 and present age of daughter = 7a - 5
According to the question,
Eight years ago, the age of Poorvi = 6a - 5 + 7a - 5 = 13a - 10
So, present age of Poorvi = 13a - 10 + 8 = 13a - 2
Since, present age of Poorvi husband = 3 (6a - 5)
The difference of present age of Poorvi husband and Poorvi = 7 (Given)

\begin{aligned} 3 (6 a - 5) - (13 a - 2) = 7 \\ \Rightarrow 18 a - 15 - 13 a + 2 = 7 \\ \Rightarrow 5 a = 20 \\ \Rightarrow a = 4 \end{aligned}

The present age of daughter
= (7a - 5)
= 7 × 4 - 5
= 23 years

46. The sum of present ages of a father and his son is 8 years more than the present age of the mother. The mother is 22 years older than the son. What will be the age of the father after 4 years?

A. 34 years

B. 36 years

C. 40 years

D. 38 years

Discuss

Solution:

Let present age of father , mother and son be x, y and z respectively
Sum of present ages of father and son = (Mother's present age + 8 years)
x + z = y + 8 years.................(i)
Mother's present age = Son's present age + 22 years)
⇒ y = z + 22 years..............(ii)
Put the value of y in equation (i) we get
x + z = z + 22 + 8
x + z = z + 30
x = 30 years
∴ Father's present age = 30 years
Age of father after four years = 30 + 4 = 34 years
∴ Required age of father = 34 years

47. Rahul is as much younger than Sagar as he is older than Purav. If the sum of the ages of Purav and Sagar is 66 years, and Sagar's age is 48 years, then what is the difference between Rahul and Purav's age ? ( in years)

A. 18

B. 15

C. 16

D. 20

Discuss

Solution:

Let the age of Rahul, Sagar and Purav be x, y and z respectively
According to the given information
Age of Sagar - Age of Rahul = Age of Rahul - Age of Purav

\begin{aligned} \Rightarrow y - x = x - z \\ \Rightarrow 2 x = y + z . . . . . . (i) \end{aligned}

Also y + z = 66 years
From (i) x = 33 years
Also as per equation (i) we have Purav's age + Sagar age = 66 years
by going through option (A) given Purav = 18, and Rahul = 33 years, Sagar = 48 years
Difference between Rahul's and Purav's age = 33 - 18 = 15 years

48. Ten years hence, the respective ratio between Simmi's age ans Niti's age will be 7 : 9. Two years ago, the respective ratio between Simmi's and Niti's age was 1 : 3. If Abhay is 4 years older then Niti, what is Abhay's present age ? (in years)

A. 8

B. 4

C. 16

D. 12

Discuss

Solution:

Let present ages of Simmi and Niti be a and b years respectively.
Ten years hence, the ratio between Simmi's age and Niti's age = 7 : 9
According to question

\frac{a + 10}{b + 10} = \frac{7}{9}

By cross multiplying we get

\begin{aligned} \Rightarrow 9 a + 90 = 7 b + 70 \\ \Rightarrow 7 b - 9 a = 20...... (i) \\ Also, \frac{a - 2}{b - 2} = \frac{1}{3} \end{aligned}

By cross multiplying we get

\begin{aligned} \Rightarrow 3 a - 6 = b - 2 \\ \Rightarrow 3 a - b = 4..... (i i) \end{aligned}

Multiplying equation (ii) by 3

9 a - 3 b = 12..... (i i i)

Adding equation (ii) and (iii) we get

\begin{aligned} - 9 a + 7 b = 20 \\ 4 b = 32 \\ b = 8 year \end{aligned}

From equation (ii) we get

\begin{aligned} a = \frac{4 + b}{3} \\ = \frac{4 + 8}{3} \\ = \frac{12}{3} \\ = 4 year \end{aligned}

Since, Abhay is 4 years older to Niti
So, Abhay's present age = 8 + 4 = 12 years

49. The sum of the present ages of a father and son is 52 years. Four years hence, the son's age will be $\frac{1}{4}$ that of the father. What will be the ratio of the ages of the son and father, 10 years from now?

A. 2 : 7

B. 2 : 5

C. 1 : 3

D. 3 : 8

Discuss

No explanation ¯\_(ツ)_/¯

50. Eight years ago, the ratio of ages of A and B was 5 : 4. The ratio of their present ages is 6 : 5. What will be the sum (in years) of the ages of A and B after 7 years from now?

A. 90

B. 80

C. 102

D. 112

Discuss

No explanation ¯\_(ツ)_/¯

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