Question 1

A person's present age is two-fifths of his mother's age. After 8 years, he will be half of his mother's age. How old is the mother now?

Accepted Answer

Problem restatement Relate present ages using a ratio; after 8 years the ratio becomes 1:2. Solve the two linear relations to find the mother's current age. Given data Let person's age = P, mother's age = M. P = (2/5)M. P + 8 = (1/2)(M + 8). Concept/Approach Substitute the ratio into the future-age relation to eliminate one variable and solve. Step-by-Step calculation (2/5)M + 8 = (1/2)(M + 8)Multiply by 10: 4M + 80 = 5M + 4080 − 40 = 5M − 4M ⇒ M = 40 Verification/Alternative Then P = (2/5)×40 = 16. After 8 years: P = 24, M = 48 → P is half of M (24 = 48/2), as required. Common pitfalls Confusing “two-fifths of mother” with “mother is two-fifths of person.” The ratio is P:M = 2:5. Final Answer 40 years

Question 2

Six years ago, the ratio of Kunal's age to Sagar's age was 6:5. Four years from now, it will be 11:10. What is Sagar's present age?

Accepted Answer

Problem restatement Two time-shifted age ratios are given (6 years ago and 4 years hence). Write equations for present ages and solve. Given data Present ages: Kunal = K, Sagar = S. (K − 6):(S − 6) = 6:5. (K + 4):(S + 4) = 11:10. Concept/Approach Convert each ratio to a linear equation and solve the simultaneous system. Step-by-Step calculation 5(K − 6) = 6(S − 6) ⇒ 5K − 30 = 6S − 36 ⇒ 5K = 6S − 6 …(1)10(K + 4) = 11(S + 4) ⇒ 10K + 40 = 11S + 44 ⇒ 10K = 11S + 4 …(2)From (1): K = (6S − 6)/5Plug in (2): 10×(6S − 6)/5 = 11S + 4 ⇒ 12S − 12 = 11S + 4 ⇒ S = 16 Verification/Alternative Then K from (1): 5K = 6×16 − 6 = 90 ⇒ K = 18. Check: 6 years ago → (12:10) = 6:5; 4 years hence → (22:20) = 11:10. Works. Common pitfalls Dropping the time shifts (−6 and +4) when forming the equations. Final Answer 16 years

Question 3

Q is as much younger than R as he is older than T. If the sum of R's and T's ages is 50 years, what is definitely the difference between R's and Q's ages?

Accepted Answer

Cannot be determined

Question 4

Present ages of Sameer and Anand are in the ratio 5:4. Three years hence, the ratio becomes 11:9. What is Anand's present age (in years)?

Accepted Answer

Problem restatement Use present ratio (5:4) and future ratio after 3 years (11:9) to solve for the common multiplier and hence Anand's age. Given data Now: Sameer = 5x, Anand = 4x. After 3 years: (5x + 3):(4x + 3) = 11:9. Concept/Approach Cross-multiply the future ratio and solve for x. Step-by-Step calculation 9(5x + 3) = 11(4x + 3)45x + 27 = 44x + 33 ⇒ x = 6Anand = 4x = 24 Verification/Alternative Future ages: Sameer 33, Anand 27 → ratio 11:9, correct. Common pitfalls Setting 5x:4x = 11:9 directly (ignores the +3 years on both sides). Final Answer 24

Question 5

Ten years ago, a father's age was three times his son's age. Ten years hence, the father's age will be twice the son's. What is the ratio of their present ages (father : son)?

Accepted Answer

Problem restatement Two linear relations connect present ages to past and future multiples. Solve for present ages and report the ratio. Given data Present ages: Father = F, Son = S. F − 10 = 3(S − 10). F + 10 = 2(S + 10). Concept/Approach Solve the simultaneous equations to get S first, then F, then form the ratio F:S. Step-by-Step calculation F − 10 = 3S − 30 ⇒ F = 3S − 20 …(1)F + 10 = 2S + 20 ⇒ F = 2S + 10 …(2)Equate (1) and (2): 3S − 20 = 2S + 10 ⇒ S = 30Then F = 2S + 10 = 70Ratio F:S = 70:30 = 7:3 Verification/Alternative Check past: 60 vs 20 (×3). Check future: 80 vs 40 (×2). Both hold. Common pitfalls Using 3(S − 10) = F + 10 (mixing past and future conditions). Final Answer 7:3

Question 6

A man is 24 years older than his son. In two years, he will be twice his son's age. What is the son's present age?

Accepted Answer

Problem restatement Express the age difference and the “twice in two years” condition as equations and solve for the son's current age. Given data Now: Father = Son + 24. In 2 years: Father + 2 = 2(Son + 2). Concept/Approach Substitute Father = Son + 24 into the future condition to solve for Son. Step-by-Step calculation (S + 24) + 2 = 2(S + 2)S + 26 = 2S + 4 ⇒ S = 22 Verification/Alternative Present ages: Son 22, Father 46. In 2 years: 24 and 48 → father is twice the son (48 = 2×24). Common pitfalls Forgetting to add 2 years to both ages in the “in two years” statement. Final Answer 22 years

Question 7

A father tells his son: “I was as old as you are now at the time of your birth.” If the father is 38 now, how old was the son five years ago?

Accepted Answer

Problem restatement At the son's birth, the father's age equaled the son's current age. Use this to find the son's present age, then subtract five years. Given data Father's current age F = 38. Let son's current age = S. At son's birth (S years ago), father's age = F − S. Statement: F − S = S. Concept/Approach Set up F − S = S ⇒ 2S = F and solve directly. Step-by-Step calculation 2S = 38 ⇒ S = 19Son's age five years ago = 19 − 5 = 14 Verification/Alternative At birth: father's age = 38 − 19 = 19, equal to the son's present age (19). Consistent. Common pitfalls Interpreting the statement as “at birth father's age equals son's age at birth” (which is zero). Final Answer 14 years

Question 8

At present, the ratio of Arun's age to Deepak's age is 4:3. After 6 years, Arun will be 26 years old. What is Deepak's present age?

Accepted Answer

Problem restatement Use Arun's future age to back out his present age, then the 4:3 ratio to get Deepak's present age. Given data Arun:Deepak = 4:3 now. Arun in 6 years = 26 ⇒ Arun now = 20. Concept/Approach If 4 parts correspond to 20 years, then 1 part is 5 years; Deepak (3 parts) is 15. Step-by-Step calculation Arun now = 26 − 6 = 20Scale factor k: 4k = 20 ⇒ k = 5Deepak now = 3k = 15 Verification/Alternative In 6 years: Deepak = 21; ratio then 26:21 = 26:21 (not required), present ratio remains 4:3. Common pitfalls Adding 6 to both ages first and then trying to compute the ratio back; simpler to get Arun now, then apply the current ratio. Final Answer 15 years

Question 9

Sachin is 7 years younger than Rahul. If their ages are in the ratio 7:9 (Sachin:Rahul), how old is Sachin?

Accepted Answer

Problem restatement Let Sachin:Rahul = 7:9 with a fixed 7-year difference Rahul − Sachin = 7. Find Sachin's age. Given data Let Sachin = 7x, Rahul = 9x. Rahul − Sachin = 7 ⇒ 9x − 7x = 7. Concept/Approach Use the ratio form with the known difference to solve for x, then compute Sachin's age. Step-by-Step calculation 2x = 7 ⇒ x = 3.5Sachin = 7x = 24.5 Verification/Alternative Rahul = 9x = 31.5; difference = 31.5 − 24.5 = 7 (matches); ratio = 24.5:31.5 = 7:9. Common pitfalls Assuming ages must be integers. Age problems can yield half-years when both a ratio and a fixed difference are imposed. Final Answer 24.5 years

Question 10

Five children are born at intervals of 3 years each. If the sum of their present ages is 50 years, what is the age of the youngest child?

Accepted Answer

Problem restatement The ages form an arithmetic progression with common difference 3. Given the sum is 50, find the youngest child's age. Given data 5 children, each 3 years apart. Sum of present ages = 50 years. Concept/Approach Let the youngest be x years. Then ages are x, x+3, x+6, x+9, x+12. Sum them and solve for x. Step-by-step calculation x + (x+3) + (x+6) + (x+9) + (x+12) = 50 5x + 30 = 50 5x = 20 → x = 4 Verification/Alternative Ages would be 4, 7, 10, 13, 16. Sum = 4 + 7 + 10 + 13 + 16 = 50 (matches). Common pitfalls Using the average (50/5 = 10) as the youngest; that is the middle term, not the youngest. Final Answer 4 years

Question 11

The present ages of three persons are in the ratio 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

Accepted Answer

Problem restatement Present ages are proportional to 4 : 7 : 9. Eight years ago their sum was 56. Determine each present age. Given data Present-age ratio = 4 : 7 : 9. Eight years ago, sum of ages = 56. Concept/Approach Let present ages be 4k, 7k, 9k. Eight years ago, subtract 8 from each and use the given sum to solve for k. Step-by-step calculation (4k − 8) + (7k − 8) + (9k − 8) = 56 20k − 24 = 56 20k = 80 → k = 4 Present ages = 4k, 7k, 9k = 16, 28, 36 (years) Verification/Alternative Eight years ago: 8, 20, 28; sum = 56 (checks out). Ratio of present ages 16:28:36 reduces to 4:7:9. Common pitfalls Forgetting to subtract 8 years from each person (subtracting only once from the total). Final Answer 16 years, 28 years, 36 years

Question 12

A is two years older than B and B is twice as old as C. If A + B + C = 27 years, how old is B?

Accepted Answer

Problem restatement Relate A, B, and C using the given age differences and total, then solve for B. Given data A = B + 2 B = 2C A + B + C = 27 Concept/Approach Express everything in terms of C and substitute into the total. Step-by-step calculation B = 2C; A = 2C + 2 (2C + 2) + 2C + C = 27 5C + 2 = 27 → 5C = 25 → C = 5 B = 2C = 10 Verification A = 12, B = 10, C = 5; sum = 27 (consistent). Common pitfalls Taking A = 2B by mistake; the statement is A is two years older than B, not twice as old. Final Answer 10 years

Question 13

The present ages of a father and his son sum to 60 years. Six years ago, the father was five times the son's age. What will be the son's age after 6 years?

Accepted Answer

Problem restatement Use a system of equations with present ages and a past ratio to find the son's current age, then add 6 years. Given data F + S = 60 (present ages of father and son). Six years ago: F − 6 = 5(S − 6). Concept/Approach Solve the linear system for S; the future age is S + 6. Step-by-step calculation F − 6 = 5S − 30 → F = 5S − 24 (5S − 24) + S = 60 6S = 84 → S = 14 After 6 years: S + 6 = 20 Verification/Alternative Present father's age F = 60 − 14 = 46. Six years ago: 40 and 8, and 40 = 5 × 8 (satisfies the condition). Common pitfalls Applying the five-times relation to present ages instead of ages six years ago. Final Answer 20 years

Question 14

Father is 'three times more than' his son Ronit in age. After 8 years, he will be two and a half times Ronit's age. After a further 8 years, how many times Ronit's age will he be?

Accepted Answer

Problem restatement Given a current multiplicative relation and a future relation (after 8 years), determine the multiplicative factor after another 8 years. Given data & Assumption Interpretation note: The phrase “three times more than” is taken literally as four times as old (common in exam parlance), i.e., F = 4S. (If interpreted as “three times as old”, results differ; see Verification.) After 8 years: F + 8 = 2.5(S + 8). Concept/Approach Use two equations to solve present ages, then compute the ratio after a further 8 years. Step-by-step calculation Let present ages be F (father), S (son). F = 4S F + 8 = 2.5(S + 8) 4S + 8 = 2.5S + 20 1.5S = 12 → S = 8, F = 32 After a further 8 years (i.e., after 16 years total): F + 16 = 48, S + 16 = 24 Required ratio = (F + 16)/(S + 16) = 48/24 = 2 Verification/Alternative If “three times more” were interpreted as “three times as old” (F = 3S), then 3S + 8 = 2.5(S + 8) gives S = 24, F = 72, and after 16 years the ratio would be 88/40 = 11/5 = 2.2. Because the prompt uses “more than”, many standardized questions expect the literal 4× reading, yielding a neat integer answer 2. Common pitfalls Confusing “times more than” with “times as old”. Always check context and expected exam convention. Computing ratio after only 8 years instead of after a further 8 years (total +16). Final Answer 2 times

Question 15

Ayesha's father was 38 when she was born. Her mother was 36 when her brother (4 years younger than Ayesha) was born. What is the age difference between her parents?

Accepted Answer

Problem restatement Translate birth-time ages into present ages using Ayesha's and her brother's age difference to find the parents' age difference. Given data Father's age at Ayesha's birth = 38. Mother's age at brother's birth = 36. Brother is 4 years younger than Ayesha. Concept/Approach Let Ayesha be a years old now. Then her father is a + 38 now. Her brother is (a − 4) now; therefore the mother is (36 + (a − 4)) = a + 32 now. Step-by-step calculation Father's present age = a + 38 Mother's present age = a + 32 Difference = (a + 38) − (a + 32) = 6 Verification The variable a cancels, so the difference is fixed at 6 years regardless of the children's current ages. Final Answer 6 years

Question 16

The ratio of a father’s age to his son’s age is 4 : 1, and the product of their ages is 196. What will be the ratio of their ages after 5 years?

Accepted Answer

Introduction / Context: Classic age problems often provide a ratio and the product (or sum). Use the ratio to write ages in terms of a variable, solve from the product, and then apply the time shift to compute the new ratio. Given Data / Assumptions: Father : Son = 4 : 1 ⇒ ages = 4x and x. Product = 196 ⇒ 4x^2 = 196. We seek (4x + 5) : (x + 5). Concept / Approach: Solve x from the product, then add 5 years to each age and simplify the resulting ratio. Step-by-Step Solution: 4x^2 = 196 ⇒ x^2 = 49 ⇒ x = 7 (ages positive).Father = 28, Son = 7.After 5 years: 33 and 12 ⇒ ratio = 33 : 12 = 11 : 4. Verification / Alternative check: Product check: 28×7 = 196; post-increment ratio simplifies correctly. Why Other Options Are Wrong: 3:1, 10:3, or 14:5 do not match the computed post-increment ages. Common Pitfalls: Using 196 as the sum instead of product, or forgetting to simplify the final ratio. Final Answer: 11 : 4

Question 17

Mr. Sohanlal is four times as old as his son at present. Four years from now, the sum of their ages will be 43 years. What is the son’s present age (in years)?

Accepted Answer

Introduction / Context: Ages problems often give a present-time multiplicative relation and a future/past sum or difference. Translate the words into linear equations and solve systematically. Given Data / Assumptions: Let son's present age = x years. Father (Mr. Sohanlal) is 4 times the son: father = 4x years. In 4 years: (x + 4) + (4x + 4) = 43. Concept / Approach: Form a single linear equation from the future sum and solve for x. Validate against given constraints (ages positive, integers typically). Step-by-Step Solution: (x + 4) + (4x + 4) = 435x + 8 = 43 ⇒ 5x = 35 ⇒ x = 7 Verification / Alternative check: Father now = 4x = 28. In 4 years: son 11, father 32; sum = 43, correct. Why Other Options Are Wrong: 5, 8, 10 produce future sums ≠ 43 under the 4x relationship. Common Pitfalls: Adding 4 only once or forgetting to add 4 to both father and son in the future-sum equation. Final Answer: 7 years.

Question 18

The present-age ratio of Vimal and Aruna is 3 : 5, and the sum of their present ages is 80 years. What will be the ratio of their ages after 10 years?

Accepted Answer

Introduction / Context: Ratios with a given sum allow us to find actual present ages using a multiplier. Future ratios follow by adding the same increment to both ages. Given Data / Assumptions: Vimal : Aruna = 3 : 5 Vimal + Aruna = 80 years Find (Vimal + 10) : (Aruna + 10) Concept / Approach: Let ages be 3k and 5k. Use 3k + 5k = 80 ⇒ k = 10. Then compute future ages and reduce the ratio. Step-by-Step Solution: 3k + 5k = 80 ⇒ k = 10Vimal = 30, Aruna = 50After 10 years ⇒ 40 : 60 = 2 : 3 Verification / Alternative check: Divide both by 20 to reduce 40 : 60 to 2 : 3, consistent. Why Other Options Are Wrong: 1 : 2 and 3 : 2 do not match 40 : 60. 3 : 5 repeats the present ratio, not the future one. Common Pitfalls: Using 80 as the future sum or adding 10k instead of 10 years to each age. Final Answer: 2 : 3.

Question 19

The present age ratio of Ashok to Pradeep is 4 : 3. Ashok will be 26 years old after 6 years. How old is Pradeep now?

Accepted Answer

Introduction / Context: Use the ratio to express present ages in terms of a multiplier, then connect with the given future age to compute the multiplier and hence the other person's age. Given Data / Assumptions: Ashok : Pradeep = 4 : 3 ⇒ Ashok = 4k, Pradeep = 3k Ashok after 6 years = 26 ⇒ current Ashok = 20 Concept / Approach: Set 4k = 20 ⇒ k = 5, then compute Pradeep = 3k. Step-by-Step Solution: 4k = 20 ⇒ k = 5Pradeep = 3k = 15 years Verification / Alternative check: Ashok 20 now; ratio 20 : 15 = 4 : 3, and Ashok in 6 years = 26, consistent. Why Other Options Are Wrong: 12, 19.5, 21 do not preserve 4 : 3 when Ashok is 20 now. Common Pitfalls: Using 26 directly in the ratio without subtracting 6 years to get the present age. Final Answer: 15 years.

Question 20

Ten years ago, Sachin was twice as old as Ajay was then. If Sachin will be 40 years old ten years from now, how old is Ajay today?

Accepted Answer

Introduction / Context: Combine past-time multiplicative information with a future-time absolute age to deduce present ages. Given Data / Assumptions: Sachin in 10 years = 40 ⇒ Sachin now = 30 10 years ago Sachin = 20, and at that time Sachin = 2 × (Ajay then) Concept / Approach: From the past relationship, find Ajay's past age, then add the elapsed time to get Ajay's present age. Step-by-Step Solution: 2 × (Ajay 10 years ago) = 20 ⇒ Ajay 10 years ago = 10Ajay now = 10 + 10 = 20 years Verification / Alternative check: Check: Ten years ago Ajay 10, Sachin 20, twice relation holds; in 10 years Sachin 40, consistent. Why Other Options Are Wrong: 10, 15, 30 contradict either the past twice relation or Sachin’s future age. Common Pitfalls: Forgetting to convert the future age into present age before using the past condition. Final Answer: 20 years.

Problems on Ages Questions