33 practice questions on Ages from the Quantitative Aptitude section of the UPSC Prelims syllabus.
33 come with a written explanation and 8 are actual previous year questions.
Try the sample set below - the answer stays hidden until you ask for it.
10 Easy19 Medium4 Hard8 from past papers
Sample questions
Q1
Previous year questioneasy
X said to Y, "At the time of your birth I was twice as old as you are at present." If the present age of X is 42 years, then consider the following statements:
1. 8 years ago, the age of X was five times the age of Y.
2. After 14 years, the age of X would be two times the age of Y.
Which of the above statements is/are correct?
A1 only
B2 only
CBoth 1 and 2
DNeither 1 nor 2
Show answer and explanation
Correct answer: B - 2 only
Let Y's present age be y. Y was born y years ago, when X's age was 42 - y, and this equals twice Y's present age: 42 - y = 2y, so y = 14. X is 42 and Y is 14. Statement 1: eight years ago X was 34 and Y was 6; five times 6 is 30, not 34, so statement 1 is incorrect. Statement 2: after 14 years X will be 56 and Y will be 28, and 56 = 2 x 28, so statement 2 is correct. Hence option (b) 2 only. Option (a) endorses the failed check, option (c) accepts both, and option (d) rejects the verified statement 2.
Q2
Previous year questionmedium
In 2002, Meenu's age was one-third of the age of Meera, whereas in 2010, Meenu's age was half the age of Meera. What is Meenu's year of birth?
A1992
B1994
C1996
D1998
Show answer and explanation
Correct answer: B - 1994
Let Meenu's age in 2002 be m, so Meera's age in 2002 is 3m. Eight years later, in 2010, Meenu is m+8 and Meera is 3m+8, and Meenu is then half of Meera: m + 8 = (3m + 8)/2. Multiply by 2: 2m + 16 = 3m + 8, so m = 8. Thus Meenu was 8 years old in 2002, giving a birth year of 2002 - 8 = 1994. Hence the answer is (b) 1994.
Q3
Previous year questionhard
The age of Mr. X last year was the square of a number and it would be the cube of a number next year. What is the least number of years he must wait for his age to become the cube of a number again?
A42
B38
C25
D16
Show answer and explanation
Correct answer: B - 38
We need last year's age to be a perfect square and next year's age to be a perfect cube, with next year = last year + 2 (since last year and next year are 2 apart). Testing small cubes: 27 = 3^3, and 27 - 2 = 25 = 5^2, a perfect square. So last year he was 25 and next year he will be 27, making his present age 26. His age becomes a cube 'again' at the next perfect cube after 27, which is 64 = 4^3. From the present age 26, reaching 64 takes 64 - 26 = 38 years. Hence (b).
Q4
Previous year questioneasy
The average age of a teacher and three students is 20 years. If all the three students are of same age and the difference between the age of the teacher and each student is 20 years, then what is the age of the teacher?
A25 years
B30 years
C35 years
D45 years
Show answer and explanation
Correct answer: C - 35 years
Total age of the four people = 4 x 20 = 80 years. Let each student be s years and the teacher be t years, with t - s = 20 (teacher is older). Then t + 3s = 80. Substituting t = s + 20: (s + 20) + 3s = 80, so 4s = 60, s = 15. Teacher's age t = 15 + 20 = 35 years.
Q5
Previous year questionmedium
The sum of the ages of 5 members comprising a family, 3 years ago was 80 years. The average age of the family today is the same as it was 3 years ago, because of an addition of a baby during the intervening period. How old is the baby?
A6 months
B1 year
C2 years
D2 years and 6 months
Show answer and explanation
Correct answer: B - 1 year
Three years ago the average age = 80/5 = 16 years. Today the original 5 members have each aged 3 years, so their combined age = 80 + 5 x 3 = 95 years. The family now has 6 members but the average is still 16, so total age today = 6 x 16 = 96 years. The baby's age = 96 - 95 = 1 year.
Q6
Previous year questionmedium
A father said to his son, "n years back I was as old as you are now. My present age is four times your age n years back." If the sum of the present ages of the father and the son is 130 years, what is the difference of their ages?
A30 years
B32 years
C34 years
D36 years
Show answer and explanation
Correct answer: A - 30 years
Let the father's present age be F and the son's present age be S. 'n years back I was as old as you are now' gives F - n = S, so n = F - S. 'My present age is four times your age n years back' gives F = 4(S - n) = 4(S - (F - S)) = 8S - 4F, so 5F = 8S. Substituting F = 8S/5 in F + S = 130 gives 13S/5 = 130, so S = 50 and F = 80. Difference = 80 - 50 = 30 years. Check: n = 30; thirty years back the father was 50 (the son's present age), and the son was 20, with 4 x 20 = 80, the father's present age.
Q7
Previous year questionmedium
Ena was born 4 years after her parents' marriage. Her mother is three years younger than her father and 24 years older than Ena, who is 13 years old. At what age did Ena's father get married?
A22 years
B23 years
C24 years
D25 years
Show answer and explanation
Correct answer: B - 23 years
Ena is 13. Her mother is 24 years older than Ena, so the mother is now 13 + 24 = 37. The father is 3 years older than the mother, so the father is now 37 + 3 = 40. Ena was born 4 years after the marriage and is 13 now, so the marriage took place 13 + 4 = 17 years ago. The father's age at marriage = 40 - 17 = 23 years. Answer (b) 23 years.
Q8
Previous year questioneasy
A father is nine times as old as his son and the mother is eight times as old as the son. The sum of the father's and the mother's age is 51 years. What is the age of the son?
(a) 7 years
(b) 5 years
(c) 4 years
(d) 3 years
A7 years
B5 years
C4 years
D3 years
Show answer and explanation
Correct answer: D - 3 years
Let the son's age be x. Then the father is 9x and the mother is 8x. Their sum is 9x + 8x = 17x, and this equals 51 years. So 17x = 51, giving x = 3. The son is 3 years old.
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