Practice MCQ Questions and Answer on Problems on Ages
21.
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
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) $$\eqalign{ & {\text{3}}\left( {6a - 5} \right) - \left( {13a - 2} \right) = 7 \cr & \Rightarrow 18a - 15 - 13a + 2 = 7 \cr & \Rightarrow 5a = 20 \cr & \Rightarrow a = 4 \cr} $$ The present age of daughter = (7a - 5) = 7 × 4 - 5 = 23 years
22.
A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?
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
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 $$\eqalign{ & \Rightarrow y - x = x - z \cr & \Rightarrow 2x = y + z......(i) \cr} $$ 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
24.
Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
(A) 2 years
(B) 4 years
(C) 6 years
(D) 8 years
Solution:
Mother's age when Ayesha's brother was born = 36 years. Father's age when Ayesha's brother was born = (38 + 4) years = 42 years. ∴ Required difference = (42 - 36) years = 6 years.
25.
The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:
(A) 5 : 2
(B) 7 : 3
(C) 9 : 2
(D) 13 : 4
Solution:
Let the ages of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] ⇒ 3x + 20 = 2x + 40 ⇒ x = 20 ∴ Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3
26.
The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
(A) 4 years
(B) 8 years
(C) 10 years
(D) None of these
Solution:
Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years. Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50 ⇒ 5x = 20 ⇒ x = 4. ∴ Age of the youngest child = x = 4 years.
27.
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
Solution:
Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years Then, $$\eqalign{ & \frac{{\left( {6x + 6} \right) + 4}}{{\left( {5x + 6} \right) + 4}} = \frac{{11}}{{10}} \cr & \Rightarrow \frac{{6x + 10}}{{5x + 10}} = \frac{{11}}{{10}} \cr & \Rightarrow 10\left( {6x + 10} \right) = 11\left( {5x + 10} \right) \cr & \Rightarrow 60x + 100 = 55x + 100 \cr & \Rightarrow 5x = 10 \cr & \Rightarrow x = 2 \cr} $$ Sagar's present age = (5x + 6) years = (5 × 2 + 6) years = 16 years
28.
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
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
29.
Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?
(A) 1 year
(B) 2 years
(C) 25 years
(D) Data inadequate
Solution:
Given that: 1. The difference of age b/w R and Q = The difference of age b/w Q and T. 2. Sum of age of R and T is 50 i.e. (R + T) = 50. Question: R - Q = ?. Explanation: R - Q = Q - T (R + T) = 2Q Now given that, (R + T) = 50 So, 50 = 2Q and therefore Q = 25. Question is (R - Q) = ? Here we know the value(age) of Q (25), but we don't know the age of R. Therefore, (R-Q) cannot be determined.
30.
The ratio between the ages of Neelam and Shiny is 5 : 6 respectively. If the ratio between the one-third age of Neelam and half of Shiny's age is 5 : 9, then what is Shiny's age = ?
(A) 25 years
(B) 30 years
(C) 36 years
(D) Cannot be determined
Solution:
Let Neelam's age be 5x years and Shiny's age be 6x years $$\eqalign{ & \left( {\frac{1}{3} \times 5x} \right):\left( {\frac{1}{2} \times 6x} \right) = 5:9 \cr & \Rightarrow \frac{{5x}}{{3 \times 3x}} = \frac{5}{9} \cr} $$ Thus, Shiny's age cannot be determined