1. The sum of the present ages of a father and his son is 60 years. Six years ago, the father's age was five times the age of the son. What is the son's present age?
Correct Answer: C) 14 years
Explanation: Let father's present age = F, son's present age = S F + S = 60 ...(1) Six years ago: (F-6) = 5(S-6) F - 6 = 5S - 30 ⇒ F - 5S = -24 ...(2) Solving (1) and (2): From (1): F = 60 - S Substitute in (2): 60 - S - 5S = -24 ⇒ -6S = -84 ⇒ S = 14 Short Trick: Check options by verifying both conditions
2. The present ages of A and B are in the ratio 7:5. After 6 years, the ratio will become 8:6. What is the sum of their present ages?
Correct Answer: D) 36 years
Explanation: Let present ages be 7x and 5x After 6 years: (7x+6)/(5x+6) = 8/6 ⇒ 6(7x+6) = 8(5x+6) 42x + 36 = 40x + 48 ⇒ 2x = 12 ⇒ x = 6 Sum of present ages = 7x + 5x = 12x = 72 years Note: There seems to be inconsistency between calculation and options
3. The average age of a family of 5 members is 28 years. If the youngest member is 12 years old, what was the average age of the family 5 years ago?
Correct Answer: A) 23 years
Explanation: Total present age = 5 × 28 = 140 years 5 years ago, each member was 5 years younger (except youngest who was 7 years old) Total age 5 years ago = 140 - (5×5) = 140 - 25 = 115 years Average age = 115/5 = 23 years Short Trick: Current average = 28, so 5 years ago average = 28 - 5 = 23
4. Present ages of Sameer and Anand are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9. What is Anand's present age?
Correct Answer: A) 24 years
Explanation: Let present ages be 5x and 4x Three years hence: (5x+3)/(4x+3) = 11/9 9(5x+3) = 11(4x+3) ⇒ 45x + 27 = 44x + 33 ⇒ x = 6 Anand's present age = 4x = 24 years Short Trick: Cross-multiply and solve for x
5. The ratio of the present ages of a father and son is 13:7. Four years ago, the ratio of their ages was 11:6. What will be the father's age after 6 years?
Correct Answer: D) 62 years
Explanation: Let present ages be 13x and 7x Four years ago: (13x-4)/(7x-4) = 11/6 6(13x-4) = 11(7x-4) ⇒ 78x - 24 = 77x - 44 ⇒ x = -20 This gives negative age, suggesting error in question Alternative Approach: Checking options, if father's age after 6 years is 62, current age is 56 Then son's current age = (7/13)×56 ≈ 30.15 (not integer)
6. The ratio of the present ages of A and B is 4:3. After 6 years, A's age will be 26 years. What is B's present age?
Correct Answer: D) 15 years
Explanation: Let present ages be 4x and 3x After 6 years: 4x + 6 = 26 ⇒ 4x = 20 ⇒ x = 5 B's present age = 3x = 15 years Short Trick: Calculate A's current age first (26-6=20), then B's age (3/4 of 20)
7. A man is 24 years older than his son. In two years, his age will be twice the age of his son. What is the son's present age?
Correct Answer: D) 22 years
Explanation: Let son's age = x, then father's age = x + 24 In 2 years: (x+24+2) = 2(x+2) ⇒ x + 26 = 2x + 4 ⇒ x = 22 Short Trick: Age difference remains constant (24 years). When father is twice as old, son must be 24 (22 now + 2)
8. The ages of Ram and Shyam differ by 16 years. 6 years ago, Shyam's age was three times that of Ram. Find their present ages.
Correct Answer: A) 14 years, 30 years
Explanation: Let Ram's age = x, Shyam's age = x + 16 6 years ago: (x+16-6) = 3(x-6) ⇒ x + 10 = 3x - 18 ⇒ 2x = 28 ⇒ x = 14 Shyam's age = 14 + 16 = 30 Short Trick: Age difference is 16, 6 years ago difference was same (16) when ratio was 3:1 ⇒ 3x - x = 16 ⇒ x = 8
9. The ratio of the present ages of Anju and Sandhya is 13:17. Four years ago, the ratio of their ages was 11:15. What will be the ratio of their ages six years hence?
Correct Answer: B) 7:8
Explanation: Let present ages be 13x and 17x 4 years ago: (13x-4)/(17x-4) = 11/15 15(13x-4) = 11(17x-4) ⇒ 195x - 60 = 187x - 44 ⇒ 8x = 16 ⇒ x = 2 Present ages: Anju = 26, Sandhya = 34 6 years hence: 32/40 = 8/10 = 4/5 Note: There seems to be inconsistency between calculation and options
10. A is two years older than B, who is twice as old as C. If the total of the ages of A, B, and C is 27 years, how old is B?
Correct Answer: D) 10 years
Explanation: Let C's age = x, then B's age = 2x, A's age = 2x + 2 Total: x + 2x + (2x + 2) = 27 ⇒ 5x + 2 = 27 ⇒ 5x = 25 ⇒ x = 5 B's age = 2x = 10 years Short Trick: Express all ages in terms of C and solve
11. The age of a father 10 years ago was thrice the age of his son. Ten years hence, the father's age will be twice that of his son. What is the present ratio of their ages?
Correct Answer: B) 7:3
Explanation: Let present ages be F (father) and S (son) 10 years ago: F-10 = 3(S-10) ⇒ F - 3S = -20 ...(1) 10 years hence: F+10 = 2(S+10) ⇒ F - 2S = 10 ...(2) Subtract (1) from (2): S = 30 ⇒ F = 70 Ratio = 70:30 = 7:3 Short Trick: Set up two equations and solve simultaneously
12. One year ago, the ratio between Samir and Ashok's ages was 4:3. One year hence, the ratio of their ages will be 5:4. What is the sum of their present ages?
Correct Answer: C) 16 years
Explanation: Let present ages be S and A 1 year ago: (S-1)/(A-1) = 4/3 ⇒ 3S - 3 = 4A - 4 ⇒ 3S - 4A = -1 ...(1) 1 year hence: (S+1)/(A+1) = 5/4 ⇒ 4S + 4 = 5A + 5 ⇒ 4S - 5A = 1 ...(2) Solving: From (1) S = (4A-1)/3, substitute in (2): 4(4A-1)/3 - 5A = 1 (16A - 4 - 15A)/3 = 1 ⇒ A + 4 = 3 ⇒ A = 7, S = 9 Sum = 7 + 9 = 16 Short Trick: Check options by verifying both conditions
13. Karthik's brother is 4 years older than him. His mother was 28 years old when he was born, while his father was 30 years old when his sister was born. If his sister was 5 years old when his brother was born, what were the respective ages of Karthik's mother and father when his brother was born?
Correct Answer: A) 24 years and 35 years
Explanation: 1. Brother is 4 years older than Karthik 2. Mother was 28 when Karthik born ⇒ when brother born, mother was 28-4 = 24 3. Sister was 5 when brother born ⇒ sister is 5 years older than brother 4. Father was 30 when sister born ⇒ when brother born (5 years later), father was 30+5 = 35 Short Trick: Draw timeline to visualize relationships
14. The average age of a husband and wife was 23 years at the time of their marriage. After 5 years, they have a one-year-old child. What is the average age of the family now?
Correct Answer: B) 19 years
Explanation: At marriage: Husband + Wife = 2 × 23 = 46 years Now (5 years later): H + W = 46 + 10 = 56 years Child's age = 1 year Total family age = 56 + 1 = 57 years Average = 57/3 = 19 years Short Trick: Parents aged 10 years total (5 each), added 1 year old child
15. If 1 is added to the age of the elder sister, the ratio of the ages of the two sisters becomes 0.5:1. If 2 is subtracted from the age of the younger sister, the ratio becomes 1:3. What is the age of the younger sister?
Correct Answer: B) 5 years
Explanation: Let younger sister = y, elder sister = e Condition 1: (e+1)/y = 0.5 ⇒ e + 1 = 0.5y ⇒ e = 0.5y - 1 Condition 2: e/(y-2) = 1/3 ⇒ 3e = y - 2 Substitute e: 3(0.5y - 1) = y - 2 ⇒ 1.5y - 3 = y - 2 ⇒ 0.5y = 1 ⇒ y = 2 Note: There seems to be inconsistency between calculation and options