# Problems on Ages- Aptitude Questions and Answers

 A father is now three times as old as his son. Five years back, he was four times as old as his son. The age of the son (in years) is? A) 12 B) 15 C) 18 D) 20 Correct Answer : 15 Explanation :Let son’s age be x years. Then, father’s age = (3x) years. Five years ago, father’s age = (3x – 5) years and son’s age = (x – 5) years. As given, Five years back, father’s age was four times So, 3x – 5 = 4 (x – 5) 3x – 5 = 4x – 20 x= 15. Today is Varun’s birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Varun today ? A) 20 B) 22 C) 25 D) 27 Correct Answer : 25 Explanation :Let Varan’s age today = x years. Then, Varan’s age after 1 year = (x + 1) years. As given, after an year he will be twice as old as he was 12 years ago Therefore his age , x + 1 = 2 (x – 12) x + 1 = 2x – 24 x = 25. A mother is 50 years old and her son is 22 years old. The mother will be twice as old as her son after ......years ? A) 4 B) 5 C) 6 D) 8 Correct Answer : 6 Explanation :Let's the after x years mother's age be twice that of his son. So (50+x)=2*(22+x) 50+x=44+2x x=6 After 6 years mother's age will be twice of his son. From today, after five years the age of father will be three times of the age of the son, while five years ago father’s age was seven times of the age of his son. Then the present ages of father and son, in years are respectively? A) 31 and 7 B) 47 and 11 C) 40 and 10 D) 30 and 11 Correct Answer : 40 and 10 Explanation :Let the father's age be x and the son's age be y As it has been, after five years x + 5 = 3*(y + 5) x - 3y = 10 ....(1) And five years ago x - 5 = 7*(y - 5) x - 7y = - 30 ....(2) After solving the above equations x = 40 and y = 10 So the present age of father and son is 40 and 10 Leela got married 6 years ago.Today her age is 1(1/4) times her age at the time of her marriage. her son’s age is 1/10 times her age. What is the present age of her son? A) 1 year B) 2 years C) 3 years D) 4 years Correct Answer : 3 years Explanation :Let the age of Leela at her marriage was x years. Present age of Leela = (x + 6) years As is given, x + 6 = (5/4)x 4x + 24 = 5x x = 24 Present age of Leela = x + 6 = 24 + 6 = 30 years Present age of Leela's son = (1/10)*30 = 3 years Five years ago, Somi’s age at that time was 1/3 rd of Amit’s age at that time. The respective ratio between Amit's age six years hence and Somi’s age twelve years hence, will be 7 : 4. What was Somi’s age three years ago? A) 13 yr B) 29 yr C) 17 yr D) 25 yr Correct Answer : 17 yr Explanation :Let the present age of Somi = X years and present age of Amit = Y years According to the question,( X − 5) = 1/3( Y − 5 ) => 3x − 15 = Y − 5 => 3x − y = 10 …(i) and Y+6 / X+12 = 7/4 => 4Y + 24 = 7X + 84 => 4Y − 7X = 60 …(ii) Now, solving Eqs. (i) and (ii), we have X = 20 years Somi’s age three years ago = 20 − 3 = 17 years The ages of Gyanendra and Jitendra are in the ratio of 12:7 respectively. After 6 years, the ratio of their ages will be 3:2 respectively . find the difference in their ages? A) 10 years B) 24 years C) 36 years D) 48 years Correct Answer : 10 years Explanation :Let,the present age of Gyanendra and Jitendra are 12x and 7x. After 6 years,the ratio of their ages, (12x+6)/(7x+6)=3/2 24x+12=21x+18 3x=6 x=2 Hence, present age of Gyanendra and Jitendra would be 24 and 14 The difference in their ages =24-14 = 10 years After 12 years, I shall be 3 times as old as I was 4 years ago. My present age is: A) 10 years B) 12 years C) 13 years D) 14 years Correct Answer : 12 years Explanation :let the present age be x Age after 12 years=x+12 Age before 4 years=x-4 Then as given, (x+12)= 3(x-4) x+12= 3x-12 24=3x-x 24=2x x=12 A group of 15 people has average age of 45 years. Two persons are excluded and the average of the remaining is increased by 5 years. What is the average age of the two persons who have been excluded? A) 20 years B) 12.5 years C) 15 years D) 10 years Correct Answer : 12.5 years Explanation :Sum of values = Average of values * Number of values Total age of 15 people = 45 * 15 = 675 years Total age of remaining people after 2 person left = (45 + 5) * (15 – 2) =50 × 13 =650 years Total age of 2 excluded people = Total age of 15 people – Total age of remaining people after 2 person left =675 – 650 =25 years Average of 2 excluded people = Total age of 2 excluded people/2 =25/2 =12.5 years The age of A is six times the age of his son. A's father is 40 years older than him. Together, they are 118 years old. What is the age of A? A) 18 years B) 36 years C) 42 years D) 76 years Correct Answer : 36 years Explanation :Let X be age of son, A's age= 6X and A's father age= 6X+40. As given X + 6X + 6X+40=118 13X=118-40 X= 78/13 X= 6, then x = 36 Hence, A's age= 6X = 6*6 = 36 years The age of two persons differ by 2 years. If the sum of their ages is equal to the square root of 144 then find the age of the elder among the two person? A) 2 B) 6 C) 7 D) 10 Correct Answer : 7 Explanation :Let the ages X and Y X-Y= 2 ....(1) X+Y= √144 => X+Y= 12 ....(2) from eq (1) and (2) X-Y= 2 X+Y= 12 ------------ 2X =14 X=7 by eq(1) X -Y =2 7-Y= 2 Y=5 The age of the elder is 7 years A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is A? A) 10 B) 12 C) 15 D) 18 Correct Answer : 12 Explanation :Let x be current age of C Then, B's age = 2x years. A's age = (2x + 2) years. Total of their ages = x + 2x + 2x + 2 = 27 5x = 25 x = 5 C is 5 years old, B's age = 2x = 2*5 = 10 years A's age = (2x + 2) = (2*5+2) = 12 years The ratio of the present ages of a father and his son is 9 : 4. After five years, the sum of their ages will be 75 years. What is the present age of the father? A) 45 years B) 40 years C) 35 years D) 30 years Correct Answer : 45 years Explanation :Let, Present age of father is 9x and age of son is 4x After five years: Age of father = 9x + 5 Age of son = 4x + 5 as is given,Sum of their ages after five years = 75 9x + 5 + 4x + 5 = 75 13x + 10 = 75 13x = 65 x = 5 Present age of father, 9x= 9 × 5 = 45 years. In a group of 7 people, the average age is found to be 17 years. Two more people joined with an average age 19 years. One person left the group whose age was 25 years. What is the new average age of the group? A) 17.5 Years B) 16.5 Years C) 18 Years D) 16 Years Correct Answer : 16.5 Years Explanation :Total age of 7 people, average age is 17 years = 7 * 17 = 119 Two new people joined with an average age 19 years = 19 * 2 = 38 Total age of 9 people = 119 + 38 = 157 Total age of 8 people after one person left the group = 157 - 25 = 132 New average age of the group = 132/8 = 16.5 years The present age of a father is 3 years more than three times the age of his son.Three years hence, father's age will be 10 years more than twice the age of the son.Find the present age of the father? A) 29 B) 31 C) 33 D) 43 Correct Answer : 33 Explanation :Let the present age be 'x' years. Then father's present age is 3x+3 years. 3 years later, age of son = x+3 As given, Three years later (3x+3)+3=2(x+3)+10 3x+6=2x+16 x=10 Hence father's present age = 3x+3 = 33 years One year ago the ratio of Ramu & Somu age was 6:7 respectively. Four years hence their ratio would become 7:8. How old is Somu? A) 32 B) 34 C) 36 D) 38 Correct Answer : 36 Explanation :Let us assume Ramu & Somu ages, 1 year ago, be 6x and 7x respectively. Given that, four years hence, this ratio would become 7:8 ⇒(6x+5):(7x+5)=7:8 ⇒8(6x+5)=7(7x+5) ⇒48x+40=49x+35 ⇒x=5 Somu's present age = 7x+1= 7×5+1=36 years