Question 1

Pushpa is twice as old as Rita was two years ago. If the difference between their present ages is 2 years, how old is Pushpa today?

Accepted Answer

Introduction / Context:This problem mixes a “twice as old as” condition referring to the past with a present-age difference. We form two equations in two unknowns. Given Data / Assumptions: Let Pushpa = P, Rita = R (present ages). P = 2(R − 2) P − R = 2 Concept / Approach:Direct substitution is simplest: solve the two simultaneous linear equations to obtain integer ages. Step-by-Step Solution: From P − R = 2 ⇒ P = R + 2Set R + 2 = 2(R − 2)R + 2 = 2R − 4 ⇒ 6 = R ⇒ R = 6Thus P = R + 2 = 8 Verification / Alternative check: Two years ago: Rita = 4, twice that is 8 ⇒ Pushpa = 8 ✓ Why Other Options Are Wrong: 6 years is Rita's present age, not Pushpa's. 10 and 12 do not satisfy both conditions simultaneously. None of these: 8 works perfectly. Common Pitfalls:Applying “twice as old” to the present age of Rita rather than her age two years ago; or assuming the older person is not specified by the difference (here, difference confirms who is older). Final Answer:8 years

Question 2

Five years ago, Vinay's age was one-third of Vikas's age. Vinay is now 17 years old. What is Vikas's present age?

Accepted Answer

Introduction / Context:A direct “years ago” ratio with one current age given. We work backward to the past and then forward for the other person's present age. Given Data / Assumptions: Vinay now = 17 5 years ago: Vinay was one-third of Vikas Concept / Approach:Compute past ages first, use the ratio to get Vikas's past age, then add the elapsed time to get his present age. Step-by-Step Solution: Vinay 5 years ago = 17 − 5 = 1212 = (1/3) × (Vikas 5 years ago) ⇒ Vikas 5 years ago = 36Therefore Vikas now = 36 + 5 = 41 Verification / Alternative check: Check: 5 years ago 41 − 5 = 36; Vinay 12 ⇒ 12 is one-third of 36 ✓ Why Other Options Are Wrong: 36 is Vikas's age five years ago, not now. 9 and 51 do not match the ratio and timeline. None of these: 41 satisfies the condition. Common Pitfalls:Forgetting to add the elapsed 5 years back after using the past ratio; confusing one-third with one-fourth or other fractions. Final Answer:41 years

Question 3

A man's age is four times that of his son today. Five years ago, the man was nine times as old as his son was then. What is the man's present age?

Accepted Answer

Introduction / Context:We combine a present multiplicative relation with a past multiplicative relation. Two equations in two unknowns lead to the solution. Given Data / Assumptions: Present: Man = 4 × Son Five years ago: Man − 5 = 9 × (Son − 5) Concept / Approach:Let present ages be M and S. Use the present relation to substitute into the past relation and solve. Step-by-Step Solution: M = 4SM − 5 = 9(S − 5)Substitute: 4S − 5 = 9S − 4540 = 5S ⇒ S = 8Therefore M = 4 × 8 = 32 Verification / Alternative check: Five years ago: M = 27, S = 3 ⇒ 27 = 9×3 ✓ Why Other Options Are Wrong: 24, 40, 44 do not satisfy both the present and past multiplicative relations. None of these: 32 meets all conditions. Common Pitfalls:Applying the 4× factor to past ages instead of present; or forgetting to subtract 5 from both ages in the past relation. Final Answer:32 years

Question 4

The sum of the present ages of a father and son is 45 years. Five years ago, the product of their ages was four times the father's age at that time. What are their present ages?

Accepted Answer

Introduction / Context:This mixes a present sum condition with a past product condition. The structure simplifies after factoring the past product equation. Given Data / Assumptions: Present ages: Father = f, Son = s f + s = 45 Five years ago: (f − 5)(s − 5) = 4(f − 5) Concept / Approach:Factor the past equation by taking (f − 5) common. This yields two possible cases; reject the infeasible one and use the sum to find both ages. Step-by-Step Solution: (f − 5)(s − 5) = 4(f − 5)(f − 5)[(s − 5) − 4] = 0 ⇒ (f − 5)(s − 9) = 0Either f = 5 (impossible for a father) or s = 9Thus s = 9 ⇒ f = 45 − 9 = 36 Verification / Alternative check: Five years ago: f = 31, s = 4 ⇒ product = 124; 4(f − 5) = 4×31 = 124 ✓ Why Other Options Are Wrong: 25,10 and 39,6 do not satisfy both conditions. None of these and 28,17 are inconsistent with the factored constraint. Common Pitfalls:Missing the factorization shortcut; choosing f = 5 despite being unrealistic; or misapplying the 5-year shift to only one age. Final Answer:36 years, 9 years

Question 5

Shyam's present age is three times that of Ramesh. After 12 years, Shyam's age will be double Ramesh's age. What is Shyam's present age?

Accepted Answer

Introduction / Context:Present and future multiplicative relations give two equations. Solving yields present ages directly. Given Data / Assumptions: Now: S = 3R After 12 years: S + 12 = 2(R + 12) Concept / Approach:Substitute the present relation into the future condition and solve for R, then compute S. Step-by-Step Solution: 3R + 12 = 2(R + 12)3R + 12 = 2R + 24 ⇒ R = 12Therefore S = 3 × 12 = 36 Verification / Alternative check: In 12 years: S = 48, R = 24 ⇒ 48 = 2×24 ✓ Why Other Options Are Wrong: 27, 32, 40 do not maintain both relations. None of these is unnecessary since 36 fits. Common Pitfalls:Using S = 2R initially; forgetting that both grow by the same amount (12) in the future relation. Final Answer:36 years

Question 6

After 10 years, A will be twice as old as B was 10 years ago. If A is currently 9 years older than B, what is B's present age?

Accepted Answer

Introduction / Context:This problem mixes a future age with a past age and adds a present-age difference. Carefully track times for both people and set up precise equations. Given Data / Assumptions: Let present ages be A and B. After 10 years: A + 10 = 2(B − 10) Now: A = B + 9 Concept / Approach:Substitute A = B + 9 into the future–past relation to produce a single linear equation in B. Solve for B, then verify with both statements. Step-by-Step Solution: (B + 9) + 10 = 2(B − 10)B + 19 = 2B − 2039 = B ⇒ B = 39Then A = B + 9 = 48 Verification / Alternative check: After 10 years: A = 58; B ten years ago: 29 ⇒ 58 = 2 × 29 ✓ Why Other Options Are Wrong: 19, 29, 49 do not satisfy both constraints. None of these is unnecessary since 39 works. Common Pitfalls:Using A + 10 = 2(B + 10) (wrong time reference for B); or mistakenly setting A − B = 9 after shifting the timeline rather than at present only. Final Answer:39 years

Question 7

A father and son together are 56 years old. In four years, the father’s age will be three times the son’s age. What are their present ages (son, father)?

Accepted Answer

Introduction / Context:Questions on ages often combine a present-time sum with a future (or past) ratio. Here, we are given the sum of a father’s and son’s ages now, and a relationship four years later. We must form linear equations and solve systematically. Given Data / Assumptions: Present sum: father + son = 56 years. In 4 years: father will be three times the son then. All ages are whole-number years; relationships are exact. Concept / Approach:Translate words into equations. Let s = son’s present age, f = father’s present age. Use simultaneous linear equations: f + s = 56 and (f + 4) = 3 * (s + 4). Step-by-Step Solution: Let s be the son’s present age and f be the father’s present age.Equation (1): f + s = 56.Equation (2): f + 4 = 3 * (s + 4) ⇒ f + 4 = 3s + 12 ⇒ f = 3s + 8.Substitute into (1): (3s + 8) + s = 56 ⇒ 4s + 8 = 56 ⇒ 4s = 48 ⇒ s = 12.Then f = 56 − 12 = 44. Verification / Alternative check: In 4 years: son = 16, father = 48. Check 48 = 3 * 16 ✔. Why Other Options Are Wrong: 16,40: In 4 years, 44 ≠ 3 * 20.14,42: In 4 years, 46 ≠ 3 * 18.18,38: Sum is 56 but 42 ≠ 3 * 22/… fails future ratio. Common Pitfalls: Mixing up “triple in 4 years” with “triple now.”Forgetting to add 4 years to both ages in the future condition. Final Answer:12 years, 44 years

Question 8

Ten years ago, A was exactly half of B in age. Their present-age ratio is 3 : 4. What is the sum of their present ages?

Accepted Answer

Introduction / Context:This age problem combines a past-time relation with a present-time ratio. We convert both statements into equations with a single parameter and compute the present ages, then sum them. Given Data / Assumptions: 10 years ago: A was half of B. Present ratio: A : B = 3 : 4. Find the sum of present ages. Concept / Approach:Let A = 3k and B = 4k at present. Use the “10 years ago” condition (A − 10) = 0.5 * (B − 10) to solve for k and then compute A + B. Step-by-Step Solution: Let present ages be A = 3k and B = 4k.Ten years ago: 3k − 10 = (1/2)(4k − 10) = 2k − 5.Therefore 3k − 10 = 2k − 5 ⇒ k = 5.Present ages: A = 15, B = 20. Sum = 35. Verification / Alternative check: Ten years ago: A = 5, B = 10; indeed A was half of B. Why Other Options Are Wrong: 8, 20, 45: Do not match the equations simultaneously.“None of these” is unnecessary because 35 is valid. Common Pitfalls: Applying the present ratio to the past directly without subtracting 10.Using A : B = 4 : 3 by mistake (order matters). Final Answer:35 years

Question 9

Jayesh is as much younger than Anil as he is older than Prasant. If Anil’s age plus Prasant’s age is 48 years, find Jayesh’s present age.

Accepted Answer

Introduction / Context:The statement “Jayesh is as much younger than Anil as he is older than Prasant” means Jayesh’s age lies exactly midway between Anil’s and Prasant’s ages. We use the midpoint idea with the given sum to compute Jayesh’s age. Given Data / Assumptions: Ages: Anil = A, Prasant = P, Jayesh = J. Condition: A − J = J − P ⇒ J is the average of A and P. Sum: A + P = 48. Concept / Approach:From A − J = J − P we get J = (A + P)/2. With A + P known, compute J directly. Step-by-Step Solution: Given A − J = J − P ⇒ 2J = A + P.A + P = 48 ⇒ 2J = 48 ⇒ J = 24. Verification / Alternative check: Pick A = 30, P = 18 (sum 48). Then J = 24 satisfies A − J = 6 and J − P = 6. Why Other Options Are Wrong: 20 or 30 contradict the midpoint requirement for sum 48.“Cannot be determined” is incorrect since data suffice. Common Pitfalls: Treating J as the difference or another ratio rather than the average.Ignoring that the sum directly pins J. Final Answer:24 years

Question 10

Three years ago, the average age of A and B was 18. Now, after C joins, the average of A, B, and C is 22. How old is C now?

Accepted Answer

Introduction / Context:Average age questions translate to total-sum calculations. A known average times the number of people yields the total of their ages at that time. We compare “three years ago” and “now with a third person” to isolate C’s present age. Given Data / Assumptions: 3 years ago: average(A, B) = 18 ⇒ sum(A, B) then = 36. Now: average(A, B, C) = 22 ⇒ sum(A, B, C) now = 66. Concept / Approach:Convert averages to totals and use aging. From 3 years ago to now, A and B each gain 3 years, so the pair’s sum increases by 6. Subtract to find C’s age. Step-by-Step Solution: Sum(A, B) three years ago = 36.Sum(A, B) now = 36 + 3 + 3 = 42.Sum(A, B, C) now = 66 ⇒ C = 66 − 42 = 24. Verification / Alternative check: If A + B = 42 now, and C = 24, then average now = (42 + 24)/3 = 22 ✔. Why Other Options Are Wrong: 27, 28, 30 do not satisfy totals/averages simultaneously. Common Pitfalls: Forgetting that both A and B aged 3 years each, adding 6 to the sum.Multiplying averages incorrectly instead of totals. Final Answer:24 years

Question 11

One year ago, Samir and Ashok’s ages were in the ratio 4 : 3. One year from now, their ages will be in the ratio 5 : 4. What is the sum of their present ages?

Accepted Answer

Introduction / Context:This is a two-condition ratio problem across different times (one year ago and one year ahead). By setting present ages as variables and applying the conditions properly (subtracting or adding 1), we solve a pair of rational equations. Given Data / Assumptions: One year ago: (S − 1) : (A − 1) = 4 : 3. One year later: (S + 1) : (A + 1) = 5 : 4. Find S + A (present sum). Concept / Approach:Convert ratios into equations and solve the system. Cross-multiplication clears denominators and yields linear equations in S and A. Step-by-Step Solution: (S − 1)/(A − 1) = 4/3 ⇒ 3(S − 1) = 4(A − 1) ⇒ 3S − 3 = 4A − 4 ⇒ 3S = 4A − 1. … (1)(S + 1)/(A + 1) = 5/4 ⇒ 4(S + 1) = 5(A + 1) ⇒ 4S + 4 = 5A + 5 ⇒ 4S = 5A + 1. … (2)From (2) and (1): (4S) − (3S) = (5A + 1) − (4A − 1) ⇒ S = A + 2.Substitute into (2): 4(A + 2) = 5A + 1 ⇒ 4A + 8 = 5A + 1 ⇒ A = 7 ⇒ S = 9.Present sum = 9 + 7 = 16. Verification / Alternative check: One year ago: 8 : 6 = 4 : 3; one year later: 10 : 8 = 5 : 4 ✔. Why Other Options Are Wrong: 12 or 15 fail one of the time-shifted ratios; “Cannot be determined” is incorrect. Common Pitfalls: Using present ages directly in ratios for past/future without adjusting ±1.Swapping numerator/denominator during cross-multiplication. Final Answer:16 years

Question 12

Present ages are in the ratio 2 : 5 (A : B). After 8 years, their ages will be in the ratio 1 : 2. What is the difference between their present ages?

Accepted Answer

Introduction / Context:Ratios of ages at two different times allow us to parameterize present ages and apply a future ratio condition. We then compute the numeric ages and their difference. Given Data / Assumptions: Now: A : B = 2 : 5 ⇒ A = 2x, B = 5x. After 8 years: (A + 8) : (B + 8) = 1 : 2. Find the present-age difference B − A. Concept / Approach:Substitute A = 2x and B = 5x into the future ratio and solve for x. The present difference is (5x − 2x). Step-by-Step Solution: (A + 8)/(B + 8) = 1/2 ⇒ 2(A + 8) = (B + 8).2(2x + 8) = 5x + 8 ⇒ 4x + 16 = 5x + 8 ⇒ x = 8.Present ages: A = 16, B = 40. Difference = 24 years. Verification / Alternative check: After 8 years: A = 24, B = 48 ⇒ 24 : 48 = 1 : 2 ✔. Why Other Options Are Wrong: 20, 26, 29 are inconsistent with the future ratio. Common Pitfalls: Forgetting to add 8 to both ages when forming the future ratio.Assuming the difference remains proportional (it does not; it is absolute). Final Answer:24 years

Question 13

Present ratio of ages is 2 : 3 (A : B). Five years hence, the ratio will be 3 : 4. What is A’s present age?

Accepted Answer

Introduction / Context:We are given present and future age ratios. Represent the present ages using a single parameter and impose the future ratio after adding 5 years to both ages. Solve for the parameter to find A’s age. Given Data / Assumptions: Now: A : B = 2 : 3 ⇒ A = 2x, B = 3x. After 5 years: (A + 5) : (B + 5) = 3 : 4. Find A’s present age. Concept / Approach:Use cross-multiplication on the future ratio to get a linear equation in x. Compute A = 2x. Step-by-Step Solution: (2x + 5)/(3x + 5) = 3/4 ⇒ 4(2x + 5) = 3(3x + 5).8x + 20 = 9x + 15 ⇒ x = 5 ⇒ A = 2x = 10. Verification / Alternative check: After 5 years: A = 15, B = 20 ⇒ 15 : 20 = 3 : 4 ✔. Why Other Options Are Wrong: 15 or 25 correspond to different x values that fail the future ratio; “Data inadequate” is false. Common Pitfalls: Using 2x : 3x directly as 3 : 4 without adding 5 years to both. Final Answer:10 years

Question 14

Present ratio of father and son is 6 : 1. After 5 years, their ratio becomes 7 : 2. What is the son’s present age?

Accepted Answer

Introduction / Context:This is a classic present-to-future ratio transformation. With present ages in a 6 : 1 ratio, we move five years ahead for both and impose a 7 : 2 ratio. Solving yields the son’s current age. Given Data / Assumptions: Now: father : son = 6 : 1 ⇒ F = 6x, S = x. After 5 years: (F + 5) : (S + 5) = 7 : 2. Find S. Concept / Approach:Substitute F and S and solve via cross-multiplication to find x and then S. Step-by-Step Solution: (6x + 5)/(x + 5) = 7/2 ⇒ 2(6x + 5) = 7(x + 5).12x + 10 = 7x + 35 ⇒ 5x = 25 ⇒ x = 5 ⇒ S = 5. Verification / Alternative check: Present ages: F = 30, S = 5. After 5 years: 35 : 10 = 7 : 2 ✔. Why Other Options Are Wrong: 6, 9, 10 do not satisfy the transformed ratio; the algebra is unique and decisive. Common Pitfalls: Adding 5 to only one person’s age instead of both. Final Answer:5 years

Question 15

One year ago, the father was four times as old as his son. Six years from now, the father will be 9 years more than twice his son’s age. What is the ratio of their present ages (father : son)?

Accepted Answer

Introduction / Context:We have two time-shifted linear relations: one from the past comparing father to son by a factor, and another from the future comparing father to twice the son plus a fixed number. Solve these equations to obtain current ages and then simplify the ratio. Given Data / Assumptions: One year ago: F − 1 = 4(S − 1). Six years later: F + 6 = 2(S + 6) + 9. Find present ratio F : S. Concept / Approach:Form linear equations in F and S and solve. The presence of constants (−1, +6, +9) requires careful algebra to avoid mistakes. Step-by-Step Solution: From the past: F − 1 = 4S − 4 ⇒ F = 4S − 3.From the future: F + 6 = 2S + 21 ⇒ F = 2S + 15.Equate: 4S − 3 = 2S + 15 ⇒ 2S = 18 ⇒ S = 9 ⇒ F = 33.Ratio F : S = 33 : 9 = 11 : 3. Verification / Alternative check: One year ago: 32 vs 8 ⇒ father = 4 × son ✔. Six years later: 39 vs 15 ⇒ 39 = 2 × 15 + 9 ✔. Why Other Options Are Wrong: 13 : 4, 12 : 5, 9 : 2 contradict one or both time-shifted conditions. Common Pitfalls: Mishandling the constants −1, +6, and +9 when translating to equations. Final Answer:11 : 3

Question 16

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

Accepted Answer

Introduction / Context:Two age relations are given at times symmetrically placed around the present: 10 years in the past and 10 years in the future. Modeling with variables and solving yields present ages and their ratio. Given Data / Assumptions: Ten years ago: F − 10 = 3(S − 10). Ten years later: F + 10 = 2(S + 10). Find present ratio F : S. Concept / Approach:Translate each condition into a linear equation in F and S, solve for S, then compute F and simplify the ratio. Step-by-Step Solution: Past: F − 10 = 3S − 30 ⇒ F = 3S − 20.Future: F + 10 = 2S + 20 ⇒ F = 2S + 10.Equate: 3S − 20 = 2S + 10 ⇒ S = 30.Then F = 2S + 10 = 70.Ratio: F : S = 70 : 30 = 7 : 3. Verification / Alternative check: Ten years ago: 60 vs 20 ⇒ father = 3 × son ✔. Ten years hence: 80 vs 40 ⇒ father = 2 × son ✔. Why Other Options Are Wrong: 8 : 5, 5 : 2, 9 : 5 do not satisfy both temporal constraints. Common Pitfalls: Solving only one condition; both must hold simultaneously.Errors when moving from “years ago / hence” to equations. Final Answer:7 : 3

Question 17

Age ratio and difference: Laxmi’s present age and her mother’s present age are in the ratio 3 : 11. The difference of their ages is 24 years. What will be the ratio of their ages after 3 years?

Accepted Answer

Introduction / Context:This problem uses basic age-ratio algebra. When a ratio and a difference are both given, we can find actual ages by interpreting each ratio “part” as an equal number of years. We then project both ages forward equally to get the required future ratio. Given Data / Assumptions: Laxmi : Mother = 3 : 11 (now) Age difference = 24 years Find ratio after 3 years Concept / Approach:If present ages are 3k and 11k, the difference 11k − 3k equals 24, which gives k. Once actual ages are known, add the same increment (3 years) to both to compute the future ratio. Step-by-Step Solution: 11k − 3k = 24 ⇒ 8k = 24 ⇒ k = 3Laxmi now = 3k = 9, Mother now = 11k = 33After 3 years: Laxmi = 12, Mother = 36 ⇒ 12 : 36 = 1 : 3 Verification / Alternative check:Difference remains 24 both now and in future (36 − 12), consistent with equal increments. The ratio simplifies cleanly to 1 : 3. Why Other Options Are Wrong:2 : 3 and 3 : 5 do not match the computed future ages 12 and 36. “None of these” is unnecessary because 1 : 3 fits exactly. Common Pitfalls:Using 24 directly as a current age; forgetting that both ages increase equally when projecting forward; or mis-simplifying the final ratio. Final Answer:1 : 3

Question 18

Three-person ages from totals: The sum of ages of A, B, and C is 185 years. Also, B is twice A, and C is 17 years older than A. Find A, B, and C (in years).

Accepted Answer

Introduction / Context:Classic linear-relationship age problems can be reduced to a single variable by expressing every person’s age in terms of A. Then a single linear equation from the total yields A, and hence B and C. Given Data / Assumptions: A + B + C = 185 B = 2A C = A + 17 Concept / Approach:Substitute the relations into the sum to solve for A. Once A is found, compute B and C directly from the given relationships. Step-by-Step Solution: A + (2A) + (A + 17) = 185 ⇒ 4A + 17 = 1854A = 168 ⇒ A = 42B = 2A = 84, C = A + 17 = 59 Verification / Alternative check:Sum check: 42 + 84 + 59 = 185 ✓. Conditions B = 2A and C = A + 17 both satisfied. Why Other Options Are Wrong:Other triples do not sum to 185 while satisfying B = 2A and C = A + 17 simultaneously. Common Pitfalls:Mixing up who is older by 17, or doubling the wrong person’s age. Always restate relationships consistently before solving. Final Answer:42, 84 and 59 years

Question 19

Current age from future value and ratio: The ratio of Surjeet’s age to Sameer’s age is 4 : 3. Surjeet will be 26 years old after 6 years. What is Sameer’s present age?

Accepted Answer

Introduction / Context:We blend a given ratio with a future-value condition. First use the future condition to get Surjeet’s present age, then use the ratio to scale down to Sameer’s present age. Given Data / Assumptions: Surjeet : Sameer = 4 : 3 (now) Surjeet in 6 years = 26 Concept / Approach:If Surjeet is 26 after 6 years, his present age is 26 − 6. Then assign 4 parts to Surjeet and 3 parts to Sameer proportionally to recover Sameer’s present age. Step-by-Step Solution: Surjeet now = 26 − 6 = 20Let common factor be k ⇒ 4k = 20 ⇒ k = 5Sameer now = 3k = 15 Verification / Alternative check:Check ratio: 20 : 15 = 4 : 3. After 6 years, Surjeet is 26, consistent with the condition. Why Other Options Are Wrong:21, 24, and 18 do not satisfy both the ratio and the future age condition simultaneously. Common Pitfalls:Using 26 directly in the ratio without first subtracting 6 to get the present age. Final Answer:15 years

Question 20

Ages from ratio and product: The present age ratio of father and son is 7 : 4, and the product of their present ages is 1008. What will be their age ratio after 6 years?

Accepted Answer

Introduction / Context:Given a ratio and a product, we find the common multiplier by taking the square root after factoring properly. Once current ages are known, adding 6 to both yields the future ratio. Given Data / Assumptions: Father : Son = 7 : 4 Product = 1008 Find ratio after 6 years Concept / Approach:Let ages be 7x and 4x. Then 28x^2 = 1008 gives x. Compute current ages, add 6 to both, and simplify the ratio. Step-by-Step Solution: 7x * 4x = 28x^2 = 1008 ⇒ x^2 = 36 ⇒ x = 6Father now = 42, Son now = 24After 6 years ⇒ 48 : 30 = 8 : 5 Verification / Alternative check:Product check: 42 * 24 = 1008; ratio update is correct after equal increments of 6 years. Why Other Options Are Wrong:5 : 3 and 7 : 4 are not the future ratio; 5 : 8 reverses the order and is incorrect. Common Pitfalls:Forgetting that adding the same years to both changes the ratio unless both ages are equal initially. Final Answer:8 : 5

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