Ages – Hard Level Questions – UGC NET Paper 1

Q1): 6 years ago, a father was 5 times as old as his son. After 6 years, the father will be 3 times as old as the son. Find the father’s present age.
A) 60 years
B) 63 years
C) 66 years
D) 69 years

Answer: C) 66 years

Explanation:

  • Step 1: Let son’s present age = S, father’s present age = F
  • Step 2: 6 years ago: F − 6 = 5(S − 6)
  • Step 3: So F = 5S − 24
  • Step 4: After 6 years: F + 6 = 3(S + 6) ⇒ F = 3S + 12
  • Step 5: 5S − 24 = 3S + 12 ⇒ 2S = 36 ⇒ S = 18
  • Final: F = 3S + 12 = 3×18 + 12 = 66, so option C is correct

Q2): 8 years ago, a mother was 6 times as old as her daughter. After 4 years, the mother will be 3 times as old as the daughter. Find the daughter’s present age.
A) 14 years
B) 15 years
C) 16 years
D) 17 years

Answer: C) 16 years

Explanation:

  • Step 1: Let daughter’s present age = D, mother’s present age = M
  • Step 2: 8 years ago: M − 8 = 6(D − 8) ⇒ M = 6D − 40
  • Step 3: After 4 years: M + 4 = 3(D + 4) ⇒ M = 3D + 8
  • Step 4: 6D − 40 = 3D + 8 ⇒ 3D = 48 ⇒ D = 16
  • Final: Daughter’s present age is 16, so option C is correct

Q3): 9 years ago, the ages of A and B were in the ratio 2 : 3. After 6 years, their ages will be in the ratio 3 : 4. Find A’s present age.
A) 36 years
B) 38 years
C) 39 years
D) 42 years

Answer: C) 39 years

Explanation:

  • Step 1: Let present ages be A = x and B = y
  • Step 2: 9 years ago ratio: (x − 9)/(y − 9) = 2/3
  • Step 3: Cross-multiply: 3(x − 9) = 2(y − 9) ⇒ 3x − 27 = 2y − 18 ⇒ 3x = 2y + 9
  • Step 4: After 6 years ratio: (x + 6)/(y + 6) = 3/4
  • Step 5: 4(x + 6) = 3(y + 6) ⇒ 4x + 24 = 3y + 18 ⇒ 4x = 3y − 6
  • Step 6: Solve the two equations ⇒ x = 39, y = 54
  • Final: A’s present age is 39 years, so option C is correct

Q4): The present ages of A and B are in the ratio 7 : 9. Their age difference is 12 years. After how many years will their ages be in the ratio 4 : 5?
A) 4 years
B) 6 years
C) 8 years
D) 10 years

Answer: B) 6 years

Explanation:

  • Step 1: Let present ages be 7k and 9k
  • Step 2: Difference = 9k − 7k = 2k = 12 ⇒ k = 6
  • Step 3: So A = 42 and B = 54
  • Step 4: After t years: (42 + t)/(54 + t) = 4/5
  • Step 5: 5(42 + t) = 4(54 + t) ⇒ 210 + 5t = 216 + 4t ⇒ t = 6
  • Final: After 6 years ratio becomes 4:5, so option B is correct

Q5): 6 years ago, the ages of A and B were in the ratio 3 : 5. After 6 years, their ages will be in the ratio 5 : 7. Find A’s present age.
A) 22 years
B) 24 years
C) 26 years
D) 28 years

Answer: B) 24 years

Explanation:

  • Step 1: Let present ages be A = x and B = y
  • Step 2: 6 years ago: (x − 6)/(y − 6) = 3/5
  • Step 3: 5(x − 6) = 3(y − 6) ⇒ 5x − 30 = 3y − 18 ⇒ 5x = 3y + 12
  • Step 4: After 6 years: (x + 6)/(y + 6) = 5/7
  • Step 5: 7(x + 6) = 5(y + 6) ⇒ 7x + 42 = 5y + 30 ⇒ 7x = 5y − 12
  • Step 6: Solve ⇒ x = 24 and y = 36
  • Final: A’s present age is 24 years, so option B is correct

Q6): The present ages of A, B, and C are in the ratio 3 : 5 : 6. After 6 years, C’s age will be equal to the sum of A’s and B’s ages 6 years ago. Find C’s present age.
A) 48 years
B) 51 years
C) 54 years
D) 57 years

Answer: C) 54 years

Explanation:

  • Step 1: Let present ages be A = 3k, B = 5k, C = 6k
  • Step 2: After 6 years: C becomes 6k + 6
  • Step 3: 6 years ago: A was 3k − 6 and B was 5k − 6
  • Step 4: Given 6k + 6 = (3k − 6) + (5k − 6)
  • Step 5: 6k + 6 = 8k − 12 ⇒ 2k = 18 ⇒ k = 9
  • Final: C = 6k = 54 years, so option C is correct

Q7): Average age of A, B, and C is 24 years. Average age of B, C, and D is 28 years. Average of A and D is 30 years. If B is 6 years older than C, find C’s present age.
A) 19 years
B) 20 years
C) 21 years
D) 22 years

Answer: C) 21 years

Explanation:

  • Step 1: From average: A + B + C = 24×3 = 72
  • Step 2: From average: B + C + D = 28×3 = 84
  • Step 3: Subtract Step 1 from Step 2: D − A = 12
  • Step 4: From average of A and D: A + D = 30×2 = 60
  • Step 5: Solve: (A + D) and (D − A) ⇒ D = 36, A = 24
  • Step 6: Now B + C = 72 − A = 72 − 24 = 48 and B = C + 6
  • Step 7: (C + 6) + C = 48 ⇒ 2C = 42 ⇒ C = 21
  • Final: C’s present age is 21 years, so option C is correct

Q8): A’s present age is equal to B’s age 6 years ago. After 6 years, the sum of their ages will be 72 years. Find A’s present age.
A) 24 years
B) 26 years
C) 27 years
D) 28 years

Answer: C) 27 years

Explanation:

  • Step 1: Let present ages be A = x and B = y
  • Step 2: Given x = y − 6
  • Step 3: After 6 years: (x + 6) + (y + 6) = 72
  • Step 4: So x + y + 12 = 72 ⇒ x + y = 60
  • Step 5: Substitute x = y − 6 ⇒ (y − 6) + y = 60 ⇒ 2y = 66 ⇒ y = 33
  • Final: x = y − 6 = 27, so option C is correct

Q9): The present ages of A and B are in the ratio 5 : 7. A’s age after 8 years will be equal to B’s age 6 years ago. Find B’s present age.
A) 45 years
B) 47 years
C) 49 years
D) 51 years

Answer: C) 49 years

Explanation:

  • Step 1: Let present ages be A = 5k and B = 7k
  • Step 2: Condition: A + 8 = B − 6
  • Step 3: So 5k + 8 = 7k − 6
  • Step 4: 14 = 2k ⇒ k = 7
  • Final: B = 7k = 49 years, so option C is correct

Q10): At present, A’s age is ( \frac{4}{5} ) of B’s age. After 10 years, A’s age will be ( \frac{5}{6} ) of B’s age. Find A’s present age.
A) 36 years
B) 38 years
C) 40 years
D) 42 years

Answer: C) 40 years

Explanation:

  • Step 1: Let B’s present age = B
  • Step 2: Given A = (4/5)B
  • Step 3: After 10 years: A + 10 = (5/6)(B + 10)
  • Step 4: Substitute A: (4/5)B + 10 = (5/6)(B + 10)
  • Step 5: Multiply by 30: 24B + 300 = 25B + 250 ⇒ B = 50
  • Final: A = (4/5)×50 = 40, so option C is correct

Q11): The sum of present ages of A and B is 66 years. B is 18 years older than A. After how many years will B be ( \frac{3}{2} ) of A?
A) 10 years
B) 11 years
C) 12 years
D) 13 years

Answer: C) 12 years

Explanation:

  • Step 1: Let A = x, then B = x + 18
  • Step 2: Given x + (x + 18) = 66 ⇒ 2x = 48 ⇒ x = 24
  • Step 3: So A = 24 and B = 42
  • Step 4: After t years: 42 + t = (3/2)(24 + t)
  • Step 5: 2(42 + t) = 3(24 + t) ⇒ 84 + 2t = 72 + 3t ⇒ t = 12
  • Final: After 12 years condition holds, so option C is correct

Q12): The sum of present ages of A, B, and C is 100 years. 4 years ago, A : B = 1 : 2. After 5 years, B : C = 3 : 4. Find C’s present age.
A) 45 years
B) 46 years
C) 47 years
D) 48 years

Answer: C) 47 years

Explanation:

  • Step 1: Let present ages be A = a, B = b, C = c with a + b + c = 100
  • Step 2: 4 years ago ratio: (a − 4)/(b − 4) = 1/2 ⇒ 2(a − 4) = (b − 4) ⇒ b = 2a − 4
  • Step 3: After 5 years ratio: (b + 5)/(c + 5) = 3/4 ⇒ 4(b + 5) = 3(c + 5)
  • Step 4: 4b + 20 = 3c + 15 ⇒ 3c = 4b + 5 ⇒ c = (4b + 5)/3
  • Step 5: Take a = 19 ⇒ b = 2(19) − 4 = 34 ⇒ c = (4×34 + 5)/3 = 141/3 = 47
  • Step 6: Check sum: 19 + 34 + 47 = 100 (fits)
  • Final: C’s present age is 47 years, so option C is correct

Q13): A father is 28 years older than his son. A grandfather is 26 years older than the father. After 6 years, grandfather will be 3 times the son’s age. Find the father’s present age.
A) 47 years
B) 48 years
C) 49 years
D) 50 years

Answer: C) 49 years

Explanation:

  • Step 1: Let son’s present age = S
  • Step 2: Father’s present age = S + 28
  • Step 3: Grandfather’s present age = (S + 28) + 26 = S + 54
  • Step 4: After 6 years: grandfather = S + 60 and son = S + 6
  • Step 5: Given S + 60 = 3(S + 6) ⇒ S + 60 = 3S + 18
  • Step 6: 42 = 2S ⇒ S = 21
  • Final: Father = S + 28 = 21 + 28 = 49, so option C is correct

Q14): 8 years ago, the ages of A and B were in the ratio 3 : 4. After 12 years, their ages will be in the ratio 5 : 6. Find B’s present age.
A) 46 years
B) 47 years
C) 48 years
D) 49 years

Answer: C) 48 years

Explanation:

  • Step 1: Let present ages be A = x and B = y
  • Step 2: 8 years ago: (x − 8)/(y − 8) = 3/4
  • Step 3: 4(x − 8) = 3(y − 8) ⇒ 4x − 32 = 3y − 24 ⇒ 4x = 3y + 8
  • Step 4: After 12 years: (x + 12)/(y + 12) = 5/6
  • Step 5: 6(x + 12) = 5(y + 12) ⇒ 6x + 72 = 5y + 60 ⇒ 6x = 5y − 12
  • Step 6: Solve the two equations ⇒ y = 48
  • Final: B’s present age is 48 years, so option C is correct

Q15): The present ages of A and B are in the ratio 5 : 6. After 7 years, their ages will be in the ratio 11 : 13. Find A’s present age.
A) 68 years
B) 70 years
C) 72 years
D) 74 years

Answer: B) 70 years

Explanation:

  • Step 1: Let present ages be A = 5k and B = 6k
  • Step 2: After 7 years: (5k + 7)/(6k + 7) = 11/13
  • Step 3: 13(5k + 7) = 11(6k + 7)
  • Step 4: 65k + 91 = 66k + 77
  • Step 5: k = 14
  • Final: A = 5k = 5×14 = 70, so option B is correct

Q16): Average age of A, B, and C is 28 years. Average age of B, C, and D is 32 years. If A : D = 3 : 5, find the average age of B and C.
A) 31 years
B) 32 years
C) 33 years
D) 34 years

Answer: C) 33 years

Explanation:

  • Step 1: From average: A + B + C = 28×3 = 84
  • Step 2: From average: B + C + D = 32×3 = 96
  • Step 3: Subtract Step 1 from Step 2: D − A = 12
  • Step 4: Given A : D = 3 : 5 ⇒ let A = 3k and D = 5k
  • Step 5: Then D − A = 2k = 12 ⇒ k = 6 ⇒ A = 18, D = 30
  • Step 6: B + C = 84 − A = 84 − 18 = 66
  • Final: Average of B and C = (B + C)/2 = 66/2 = 33, so option C is correct

Q17): A is 4 years less than 3 times B. After 5 years, A will be twice B (at that time). Find A’s present age.
A) 21 years
B) 22 years
C) 23 years
D) 24 years

Answer: C) 23 years

Explanation:

  • Step 1: Let B’s present age = b
  • Step 2: Given A = 3b − 4
  • Step 3: After 5 years: A + 5 = 2(B + 5)
  • Step 4: Substitute A: (3b − 4) + 5 = 2(b + 5)
  • Step 5: 3b + 1 = 2b + 10 ⇒ b = 9
  • Final: A = 3b − 4 = 27 − 4 = 23, so option C is correct

Q18): The present ages of A and B are in the ratio 3 : 4 and their sum is 70 years. After how many years will their ages be in the ratio 5 : 6?
A) 18 years
B) 19 years
C) 20 years
D) 21 years

Answer: C) 20 years

Explanation:

  • Step 1: Let present ages be 3k and 4k
  • Step 2: Given 3k + 4k = 70 ⇒ 7k = 70 ⇒ k = 10
  • Step 3: So A = 30 and B = 40
  • Step 4: After t years: (30 + t)/(40 + t) = 5/6
  • Step 5: 6(30 + t) = 5(40 + t) ⇒ 180 + 6t = 200 + 5t ⇒ t = 20
  • Final: After 20 years ratio becomes 5:6, so option C is correct

Q19): 5 years ago, the ages of A and B were in the ratio 3 : 5. After 8 years, their ages will be in the ratio 2 : 3. Find B’s present age.
A) 66 years
B) 68 years
C) 70 years
D) 72 years

Answer: C) 70 years

Explanation:

  • Step 1: Let present ages be A = x and B = y
  • Step 2: 5 years ago: (x − 5)/(y − 5) = 3/5
  • Step 3: 5(x − 5) = 3(y − 5) ⇒ 5x − 25 = 3y − 15 ⇒ 5x = 3y + 10
  • Step 4: After 8 years: (x + 8)/(y + 8) = 2/3
  • Step 5: 3(x + 8) = 2(y + 8) ⇒ 3x + 24 = 2y + 16 ⇒ 3x = 2y − 8
  • Step 6: Solve ⇒ y = 70
  • Final: B’s present age is 70 years, so option C is correct

Q20): A is 5 years younger than C, and B is 5 years older than C. If A : B = 6 : 7, after how many years will A : B become 9 : 10?
A) 25 years
B) 28 years
C) 30 years
D) 32 years

Answer: C) 30 years

Explanation:

  • Step 1: Let C’s present age = c
  • Step 2: Then A = c − 5 and B = c + 5
  • Step 3: Given (c − 5)/(c + 5) = 6/7
  • Step 4: 7(c − 5) = 6(c + 5) ⇒ 7c − 35 = 6c + 30 ⇒ c = 65
  • Step 5: So A = 60 and B = 70
  • Step 6: After t years: (60 + t)/(70 + t) = 9/10 ⇒ 10(60 + t) = 9(70 + t)
  • Step 7: 600 + 10t = 630 + 9t ⇒ t = 30
  • Final: After 30 years ratio becomes 9:10, so option C is correct

This Tutorial is Related to: Ages, Ages Mcqs, Ages Questions, Average Age Problems, Father Son Age, Grandfather Father Son, Hard Level, Mother Daughter Age, Past And Future Ages, Pyq Pattern, Ratio Of Ages, Ugc Net Paper 1, Unit 5

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