Practice Questions
Concept Explanation
Age problems use ratios that change over time. If A:B = 3:5 now, after t years add t to each part.
After t years: (3k + t) : (5k + t).
Set up equations from sum of ages, difference, or future/past ratio conditions.
-
Q1 EasyAges of A and B are in the ratio 3 : 5. If their sum is 48 years, what is A's age?Explanation3k + 5k = 48 → k = 6. A = 18 years.
-
Q2 EasyPresent ages are in the ratio 4 : 7 and their sum is 55. What is the older person's age?Explanation11k = 55 → k = 5. Older = 35 years.
-
Q3 EasyAges are in the ratio 2 : 3 and their sum is 40 years. What is the older person's age?Explanation5k = 40 → k = 8. Older = 24 years.
-
Q4 EasyThree persons have ages in the ratio 2 : 3 : 4 and sum 54 years. What is the middle age?Explanation9k = 54 → k = 6. Middle = 18 years.
-
Q5 EasyA is twice as old as B. Their sum is 36 years. What is B's age?Explanation2B + B = 36 → B = 12 years.
-
Q6 MediumThe present ages of three persons are in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Their present ages are (in years):Explanation4k+7k+9k−24=56 → 20k=80 → k=4. Ages 16, 28, 36.
-
Q7 MediumA father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 48 years now, the son's age five years back was:ExplanationFather was son's present age at son's birth → father = 2 × son. 2s = 48 → s = 24. Five years back son was 19.
-
Q8 MediumAges are in the ratio 5 : 3 and their difference is 12 years. What are the ages?Explanation2k = 12 → k = 6. Ages are 30 and 18 years.
-
Q9 MediumMother : daughter = 11 : 3. Difference of ages is 32 years. What is the daughter's age?Explanation8k = 32 → k = 4. Daughter = 12 years.
-
Q10 MediumFather is 40 and son is 10. After how many years will the ratio of their ages be 3 : 1?Explanation(40+t)/(10+t)=3/1 → 40+t=30+3t → 2t=10 → t=5 years.
-
Q11 HardThe ratio of present ages of two brothers is 1 : 2 and 5 years back the ratio was 1 : 3. What will be the ratio of their ages after 5 years?ExplanationLet ages be x and 2x. Then (x−5):(2x−5)=1:3 → 3x−15=2x−5 → x=10. Ages 10 and 20. After 5 years: 15:25 = 3:5.
-
Q12 HardThe ages of two persons differ by 16 years. If 6 years ago, the elder one was 3 times as old as the younger one, find their present ages.ExplanationLet younger = x, elder = x+16. Then x+16−6 = 3(x−6) → x+10 = 3x−18 → 2x = 28 → x = 14. Ages 14 and 30.
-
Q13 HardThe ratio of the ages of a man and his wife is 4 : 3. After 4 years, this ratio will be 9 : 7. If at the time of marriage, the ratio was 5 : 3, then how many years ago were they married?Explanation4k+4 / 3k+4 = 9/7 → 28k+28 = 27k+36 → k=8. Ages 32 and 24. Marriage: (32−t)/(24−t)=5/3 → 96−3t=120−5t → 2t=24 → t=12.
-
Q14 HardThe ratio of the present ages of a father and his son is 7 : 2. After 5 years, the ratio becomes 8 : 3. What is the son's present age?Explanation(7k+5)/(2k+5)=8/3 → 21k+15 = 16k+40 → 5k = 25 → k = 5. Son's present age = 2k = 10 years.
-
DS1 Easy
In a campus age-problem drill, what is A's present age?
Statement IA and B are in the ratio 4 : 5.
Statement IIThe sum of their ages is 54 years.
ExplanationTogether: A = 24 years and B = 30 years. -
DS2 Easy
What will the age ratio be after 5 years?
Statement IPresent ages are 20 and 30 years.
Statement IIBoth ages increase by 5 years over the period.
ExplanationTogether: after 5 years ages are 25 and 35 → ratio 5 : 7.
-
DS3 Medium
What is the difference between their ages?
Statement IPresent ages are in the ratio 7 : 9.
Statement IIThe sum of their ages is 80 years.
ExplanationTogether: 16k = 80 → k = 5. Difference = 10 years. -
DS4 Hard
Is the older person above 40 years of age?
Statement IThe ratio of their ages is 5 : 8.
Statement IIThe sum of their ages is 65 years.
ExplanationTogether: ages are 25 and 40. The older person is 40, not above 40 — question is answerable.