Problems on Ages Questions and Answers

Q: A's age 4 years ago was four times the present age of 'B'. At present, C's age is thrice the age of 'B'. Also 'C' is 24 years younger than 'A'. What is the present age of 'C' ?

C is 60 years old.Let B's present age be b. Then C = 3b, and since C is 24 years younger than A, A = 3b + 24. Four years ago A was \(3b + 20\), which equals four times B's present age:\[ \begin{aligned} 3b + 20 &= 4b \\ b &= 20 \end{aligned} \]So B is 20, C is \(3 \times 20 = 60\), and A is 84. Check: four years ago A was 80, which is four times 20.The other options fail this check; for example C = 54 gives B = 18 and A = 78, and 74 is not four times 18.

Q: Arun is three years older than Varun. Eight years ago, \(\frac{5}{6}\)th of Arun's age exceeded \(\frac{3}{5}\)th of Varun's age by 6 years. If the present age of Varun is x years, then the value of x can be determined by solving the equation :

The equation is \(\frac{5}{6}(x - 5) - \frac{3}{5}(x - 8) = 6\).Varun is x years old now, so Arun is x + 3. Eight years ago their ages were:\[ \begin{aligned} \text{Arun} &= (x + 3) - 8 = x - 5 \\ \text{Varun} &= x - 8 \end{aligned} \]Five-sixths of Arun's age then exceeded three-fifths of Varun's by 6, which is the first equation. The second swaps the two past ages, the third and fourth attach the fractions to the wrong person and use the wrong ages.

Q: Shalini's mother is 12 years more than twice of Shalini's age. After 8 years, she will be 20 years less than three times of Shalini's age. Then the age of Shalini's mother is :

Shalini's mother is 44 years old.Let Shalini's present age be \(s\). Then the mother's age is \(2s + 12\). After 8 years the mother is 20 years less than three times Shalini's age then:\[ \begin{aligned} 2s + 12 + 8 &= 3(s + 8) - 20 \\ 2s + 20 &= 3s + 4 \\ s &= 16 \end{aligned} \]So the mother is \(2 \times 16 + 12 = 44\) years. Check: in 8 years she will be 52 and Shalini 24, and \(3 \times 24 - 20 = 52\).46, 48 and 50 do not satisfy both conditions; for example 48 would make Shalini 18, and then in 8 years 56 is not \(3 \times 26 - 20 = 58\).

Q: Given below are two statements:Statement I : Four year ago, the ratio of ages of Neeru and Divya was 3:4, average of the present age of Neeru, Divya and Kusum is 26 years. Also, Kusum is 11 years younger than Divya. The present age of Divya is 38 years.Statement II : The age of mother today is thrice that of her daughter. After 10 years, the age of the mother will be twice that of her daughter. The present age of the daughter is 30 years.In the light of the above statements, choose the correct answer from the options given below:

Both Statement I and Statement II are false.Statement I: four years ago Neeru and Divya were 3x and 4x, so now they are \(3x + 4\) and \(4x + 4\), and Kusum is \(4x + 4 - 11 = 4x - 7\). Their total is \(3 \times 26 = 78\).\[ \begin{aligned} (3x + 4) + (4x + 4) + (4x - 7) &= 78 \\ 11x + 1 &= 78 \Rightarrow x = 7 \end{aligned} \]So Divya is \(4 \times 7 + 4 = 32\), not 38.Statement II: with the daughter d and mother 3d, \(3d + 10 = 2(d + 10)\) gives d = 10, not 30. Both statements are false.

Q: The sum of the ages of 2 brothers is 50. Ten years ago, the elder brother was twice the age of the younger. What is the present age of the elder?

The elder brother is 30 years old.Let the younger be \(y\), so the elder is \(50 - y\). Ten years ago the elder was twice the younger:\[ \begin{aligned} 40 - y &= 2(y - 10) \\ 60 &= 3y \Rightarrow y = 20 \end{aligned} \]The elder is 30. Check: ten years ago they were 20 and 10. 20 years is the younger brother's age, the likely slip.

Q: The ratio of Mother's age to the Son's age is 11:6. Five years ago the Mother's age was double the age of the Son. How many times the Son's age will the Mother's age be twenty years from now?

Twenty years from now the mother will be 1.5 times the son's age.Let the present ages be 11x and 6x.\[ \begin{aligned} 11x - 5 &= 2(6x - 5) \\ 11x - 5 &= 12x - 10 \\ x &= 5 \end{aligned} \]So the mother is 55 and the son 30 now. In twenty years they will be 75 and 50.\[ \frac{75}{50} = 1.5 \]Check: five years ago they were 50 and 25, and 50 is double 25. The other options come from using the wrong time, for example 2 times is the ratio five years ago.

Q: Arun's present age is one third of the age of his father. After 15 years, his age will be one half of age of his father. How old is Arun's father at present ?

Arun's father is 45 years old.Let the father's present age be \(F\), so Arun is \(F/3\). In 15 years Arun will be half his father's age:\[ \begin{aligned} \tfrac{F}{3} + 15 &= \tfrac{1}{2}(F + 15) \\ 2F + 90 &= 3F + 45 \\ F &= 45 \end{aligned} \]Check: Arun is 15 now; in 15 years he will be 30 and his father 60, exactly half. The option 15 is Arun's age, not his father's.

Q: 15 years ago, the mother's age was twice the daughter's age. If 3 years from now, the sum of their ages will be 99, what is the difference between their present ages ?

The difference between their present ages is 21 years.Let the mother's present age be \(m\) and the daughter's \(d\).\[ \begin{aligned} m - 15 &= 2(d - 15) \\ m &= 2d - 15 \end{aligned} \]Three years from now their ages add up to 99:\[ \begin{aligned} (m+3) + (d+3) &= 99 \\ m + d &= 93 \\ (2d - 15) + d &= 93 \\ d &= 36,\ m = 57 \end{aligned} \]So the difference is \(57 - 36 = 21\) years. As a check, 15 years ago they were 42 and 21, and 42 is twice 21. The difference between two ages never changes, so the other options cannot be right once 42 and 21 check out.

Q: Neha's father's age is 5 years more than three times Neha's age. Neha's father is 44 years old, then Neha's age will be :

Neha is 13 years old.Let Neha's age be \(n\). Her father's age is five more than three times hers:\[ \begin{aligned} 3n + 5 &= 44 \\ 3n &= 39 \\ n &= 13 \end{aligned} \]Check: three times 13 is 39, and 39 + 5 = 44. The option 39 years is the value of \(3n\), a step short of the answer. 12 years would give a father of 41, and 8 years a father of 29.

Important Instructions

A's age 4 years ago was four times the present age of 'B'. At present, C's age is thrice the age of 'B'. Also 'C' is 24 years younger than 'A'. What is the present age of 'C' ?

A.42 years
B.60 years
C.54 years
D.30 years

Exam Year(s)

CBSE Assistant Secretary - 2024,

Answer: B

C is 60 years old.

Let B's present age be b. Then C = 3b, and since C is 24 years younger than A, A = 3b + 24. Four years ago A was \(3b + 20\), which equals four times B's present age:

\[ \begin{aligned} 3b + 20 &= 4b \\ b &= 20 \end{aligned} \]

So B is 20, C is \(3 \times 20 = 60\), and A is 84. Check: four years ago A was 80, which is four times 20.

The other options fail this check; for example C = 54 gives B = 18 and A = 78, and 74 is not four times 18.

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Arun is three years older than Varun. Eight years ago, \(\frac{5}{6}\)th of Arun's age exceeded \(\frac{3}{5}\)th of Varun's age by 6 years. If the present age of Varun is x years, then the value of x can be determined by solving the equation :

A.\(\frac{5}{6}(x - 5) - \frac{3}{5}(x - 8) = 6\)
B.\(\frac{5}{6}(x - 8) - \frac{3}{5}(x - 5) = 6\)
C.\(\frac{3}{5}(x + 5) - \frac{5}{6}(x - 8) = 6\)
D.\(\frac{3}{5}(x + 3) - \frac{5}{6}(x - 8) = 6\)

Exam Year(s)

CTET - 2024,

Answer: A

The equation is \(\frac{5}{6}(x - 5) - \frac{3}{5}(x - 8) = 6\).

Varun is x years old now, so Arun is x + 3. Eight years ago their ages were:

\[ \begin{aligned} \text{Arun} &= (x + 3) - 8 = x - 5 \\ \text{Varun} &= x - 8 \end{aligned} \]

Five-sixths of Arun's age then exceeded three-fifths of Varun's by 6, which is the first equation. The second swaps the two past ages, the third and fourth attach the fractions to the wrong person and use the wrong ages.

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The ratio of ages (in years) of Ajit and Raghav, five years ago, was 3 : 5. After 4 years from now, the ratio of their ages (in years) will be 15 : 22. What will be the age (in years) of Raghav, after 6 years from now?

A.43
B.45
C.46
D.47

Exam Year(s)

DSSSB - 2023,

Answer: C

Raghav will be 46 years old. Let the ages five years ago be 3k and 5k. After 4 years from now (9 years after that date) their ages are 3k + 9 and 5k + 9, in the ratio 15 : 22. \[22(3k + 9) = 15(5k + 9)\] \[66k + 198 = 75k + 135\] \[9k = 63, k = 7\] Raghav's age five years ago was 35, so he is 40 now and 46 after 6 years. Check: Ajit is 26 now, and after 4 years the ages are 30 and 44, a ratio of 15 : 22.

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Shalini's mother is 12 years more than twice of Shalini's age. After 8 years, she will be 20 years less than three times of Shalini's age. Then the age of Shalini's mother is :

A.44 years
B.46 years
C.48 years
D.50 years

Exam Year(s)

HPPSC HPAS - 2025,

Answer: A

Shalini's mother is 44 years old.

Let Shalini's present age be \(s\). Then the mother's age is \(2s + 12\). After 8 years the mother is 20 years less than three times Shalini's age then:

\[ \begin{aligned} 2s + 12 + 8 &= 3(s + 8) - 20 \\ 2s + 20 &= 3s + 4 \\ s &= 16 \end{aligned} \]

So the mother is \(2 \times 16 + 12 = 44\) years. Check: in 8 years she will be 52 and Shalini 24, and \(3 \times 24 - 20 = 52\).

46, 48 and 50 do not satisfy both conditions; for example 48 would make Shalini 18, and then in 8 years 56 is not \(3 \times 26 - 20 = 58\).

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Given below are two statements:

Statement I : Four year ago, the ratio of ages of Neeru and Divya was 3:4, average of the present age of Neeru, Divya and Kusum is 26 years. Also, Kusum is 11 years younger than Divya. The present age of Divya is 38 years.
Statement II : The age of mother today is thrice that of her daughter. After 10 years, the age of the mother will be twice that of her daughter. The present age of the daughter is 30 years.

In the light of the above statements, choose the correct answer from the options given below:

A.Both Statement I and Statement II are true.
B.Both Statement I and Statement II are false.
C.Statement I is true but Statement II is false.
D.Statement I is false but Statement II is true.

Exam Year(s)

Haryana Civil Services - 2026, HPSC - 2026,

Answer: B

Both Statement I and Statement II are false.

Statement I: four years ago Neeru and Divya were 3x and 4x, so now they are \(3x + 4\) and \(4x + 4\), and Kusum is \(4x + 4 - 11 = 4x - 7\). Their total is \(3 \times 26 = 78\).

\[ \begin{aligned} (3x + 4) + (4x + 4) + (4x - 7) &= 78 \\ 11x + 1 &= 78 \Rightarrow x = 7 \end{aligned} \]

So Divya is \(4 \times 7 + 4 = 32\), not 38.

Statement II: with the daughter d and mother 3d, \(3d + 10 = 2(d + 10)\) gives d = 10, not 30. Both statements are false.

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The sum of the ages of 2 brothers is 50. Ten years ago, the elder brother was twice the age of the younger. What is the present age of the elder?

A.30 years
B.35 years
C.20 years
D.25 years

Exam Year(s)

ISRO Assistant - 2023,

Answer: A

The elder brother is 30 years old.

Let the younger be \(y\), so the elder is \(50 - y\). Ten years ago the elder was twice the younger:

\[ \begin{aligned} 40 - y &= 2(y - 10) \\ 60 &= 3y \Rightarrow y = 20 \end{aligned} \]

The elder is 30. Check: ten years ago they were 20 and 10. 20 years is the younger brother's age, the likely slip.

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The ratio of Mother's age to the Son's age is 11:6. Five years ago the Mother's age was double the age of the Son. How many times the Son's age will the Mother's age be twenty years from now?

A.2.25 times
B.2 times
C.1.75 times
D.1.5 times

Exam Year(s)

Kerala PSC KAS - 2020,

Answer: D

Twenty years from now the mother will be 1.5 times the son's age.

Let the present ages be 11x and 6x.

\[ \begin{aligned} 11x - 5 &= 2(6x - 5) \\ 11x - 5 &= 12x - 10 \\ x &= 5 \end{aligned} \]

So the mother is 55 and the son 30 now. In twenty years they will be 75 and 50.

\[ \frac{75}{50} = 1.5 \]

Check: five years ago they were 50 and 25, and 50 is double 25. The other options come from using the wrong time, for example 2 times is the ratio five years ago.

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Arun's present age is one third of the age of his father. After 15 years, his age will be one half of age of his father. How old is Arun's father at present ?

A.30
B.15
C.60
D.45

Exam Year(s)

Kerala PSC KAS - 2020,

Answer: D

Arun's father is 45 years old.

Let the father's present age be \(F\), so Arun is \(F/3\). In 15 years Arun will be half his father's age:

\[ \begin{aligned} \tfrac{F}{3} + 15 &= \tfrac{1}{2}(F + 15) \\ 2F + 90 &= 3F + 45 \\ F &= 45 \end{aligned} \]

Check: Arun is 15 now; in 15 years he will be 30 and his father 60, exactly half. The option 15 is Arun's age, not his father's.

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15 years ago, the mother's age was twice the daughter's age. If 3 years from now, the sum of their ages will be 99, what is the difference between their present ages ?

A.19 years
B.21 years
C.23 years
D.25 years

Exam Year(s)

Kerala PSC KAS - 2025,

Answer: B

The difference between their present ages is 21 years.

Let the mother's present age be \(m\) and the daughter's \(d\).

\[ \begin{aligned} m - 15 &= 2(d - 15) \\ m &= 2d - 15 \end{aligned} \]

Three years from now their ages add up to 99:

\[ \begin{aligned} (m+3) + (d+3) &= 99 \\ m + d &= 93 \\ (2d - 15) + d &= 93 \\ d &= 36,\ m = 57 \end{aligned} \]

So the difference is \(57 - 36 = 21\) years. As a check, 15 years ago they were 42 and 21, and 42 is twice 21. The difference between two ages never changes, so the other options cannot be right once 42 and 21 check out.

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10.

Neha's father's age is 5 years more than three times Neha's age. Neha's father is 44 years old, then Neha's age will be :

A.39 years
B.13 years
C.12 years
D.8 years

Exam Year(s)

MPPSC Forest Service - 2023,

Answer: B

Neha is 13 years old.

Let Neha's age be \(n\). Her father's age is five more than three times hers:

\[ \begin{aligned} 3n + 5 &= 44 \\ 3n &= 39 \\ n &= 13 \end{aligned} \]

Check: three times 13 is 39, and 39 + 5 = 44. The option 39 years is the value of \(3n\), a step short of the answer. 12 years would give a father of 41, and 8 years a father of 29.

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