Q1): 3 years ago, Rahul was 12 years old. What is his present age?
A) 14 years
B) 15 years
C) 16 years
D) 18 years
Answer: C) 15 years
Explanation:
- Step 1: 3 years ago age = 12
- Step 2: Present age = 12 + 3
- Step 3: Present age = 15
- Final: Adding back 3 years gives the current age, so option C is correct
Q2): A father is 3 times as old as his son. After 12 years, the father will be 2 times as old as the son. Find the son’s present age.
A) 10 years
B) 12 years
C) 14 years
D) 16 years
Answer: B) 12 years
Explanation:
- Step 1: Let son’s present age = x
- Step 2: Father’s present age = 3x
- Step 3: After 12 years: father = 3x + 12, son = x + 12
- Step 4: Given 3x + 12 = 2(x + 12)
- Step 5: 3x + 12 = 2x + 24 → x = 12
- Final: Son’s present age is 12 years, so option B is correct
Q3): The present ages of A and B are in the ratio 4 : 5. After 6 years, their ages add up to 84. Find A’s present age.
A) 28 years
B) 30 years
C) 32 years
D) 34 years
Answer: C) 32 years
Explanation:
- Step 1: Let present ages be 4x and 5x
- Step 2: After 6 years: ages become (4x + 6) and (5x + 6)
- Step 3: Sum after 6 years = 84
- Step 4: (4x + 6) + (5x + 6) = 84
- Step 5: 9x + 12 = 84 → 9x = 72 → x = 8
- Step 6: A’s present age = 4x = 4 × 8 = 32
- Final: A is 32 years, so option C is correct
Q4): The difference between the ages of two persons is 12 years. After 4 years, the younger : older age ratio becomes 3 : 4. Find the younger person’s present age.
A) 28 years
B) 30 years
C) 32 years
D) 34 years
Answer: C) 32 years
Explanation:
- Step 1: Let younger’s present age = y
- Step 2: Older’s present age = y + 12
- Step 3: After 4 years: younger = y + 4, older = y + 16
- Step 4: Given (y + 4) : (y + 16) = 3 : 4
- Step 5: 4(y + 4) = 3(y + 16)
- Step 6: 4y + 16 = 3y + 48 → y = 32
- Final: Younger is 32 years, so option C is correct
Q5): A mother is 4 times as old as her daughter. After 12 years, the mother will be twice as old as the daughter. Find the daughter’s present age.
A) 5 years
B) 6 years
C) 7 years
D) 8 years
Answer: B) 6 years
Explanation:
- Step 1: Let daughter’s present age = d
- Step 2: Mother’s present age = 4d
- Step 3: After 12 years: mother = 4d + 12, daughter = d + 12
- Step 4: Given 4d + 12 = 2(d + 12)
- Step 5: 4d + 12 = 2d + 24 → 2d = 12 → d = 6
- Final: Daughter is 6 years, so option B is correct
Q6): The average age of 4 friends is 24 years. One friend aged 30 leaves and a new friend aged 22 joins. What is the new average age?
A) 21 years
B) 22 years
C) 23 years
D) 24 years
Answer: B) 22 years
Explanation:
- Step 1: Total age of 4 friends = 24 × 4 = 96
- Step 2: After 30 leaves: total becomes 96 − 30 = 66
- Step 3: After 22 joins: total becomes 66 + 22 = 88
- Step 4: New average = 88 ÷ 4 = 22
- Final: New average is 22 years, so option B is correct
Q7): Ram’s age is ( \frac{2}{3} ) of Shyam’s age. After 6 years, Ram’s age becomes ( \frac{3}{4} ) of Shyam’s age. Find Ram’s present age.
A) 10 years
B) 12 years
C) 14 years
D) 16 years
Answer: B) 12 years
Explanation:
- Step 1: Let Shyam = 3k, Ram = 2k (from 2/3 relation)
- Step 2: After 6 years: Ram = 2k + 6, Shyam = 3k + 6
- Step 3: Given 2k + 6 = (3/4)(3k + 6)
- Step 4: 2k + 6 = (9k + 18)/4
- Step 5: Multiply by 4: 8k + 24 = 9k + 18 → k = 6
- Step 6: Ram’s present age = 2k = 12
- Final: Ram is 12 years, so option B is correct
Q8): The sum of ages of A and B is 58 years. 5 years ago, A was 3 times B. Find A’s present age.
A) 39 years
B) 40 years
C) 41 years
D) 42 years
Answer: C) 41 years
Explanation:
- Step 1: Let present ages be A and B
- Step 2: Given A + B = 58
- Step 3: 5 years ago: A − 5 = 3(B − 5)
- Step 4: A − 5 = 3B − 15 → A = 3B − 10
- Step 5: Substitute: (3B − 10) + B = 58 → 4B = 68 → B = 17
- Step 6: A = 58 − 17 = 41
- Final: A is 41 years, so option C is correct
Q9): A person’s present age is double his age 10 years ago. What is his present age?
A) 18 years
B) 20 years
C) 22 years
D) 24 years
Answer: B) 20 years
Explanation:
- Step 1: Let present age = x
- Step 2: Age 10 years ago = x − 10
- Step 3: Given x = 2(x − 10)
- Step 4: x = 2x − 20 → x = 20
- Final: Present age is 20 years, so option B is correct
Q10): In 8 years, a person’s age will be 3 times his age 8 years ago. What is his present age?
A) 14 years
B) 15 years
C) 16 years
D) 18 years
Answer: C) 16 years
Explanation:
- Step 1: Let present age = x
- Step 2: Age after 8 years = x + 8
- Step 3: Age 8 years ago = x − 8
- Step 4: Given x + 8 = 3(x − 8)
- Step 5: x + 8 = 3x − 24 → 2x = 32 → x = 16
- Final: Present age is 16 years, so option C is correct
Q11): The ratio of father’s age to son’s age is 5 : 2. If the difference of their ages is 33 years, find the father’s age.
A) 44 years
B) 50 years
C) 55 years
D) 60 years
Answer: C) 55 years
Explanation:
- Step 1: Let ages be 5k and 2k
- Step 2: Difference = 5k − 2k = 3k
- Step 3: Given 3k = 33 → k = 11
- Step 4: Father’s age = 5k = 5 × 11 = 55
- Final: Father is 55 years, so option C is correct
Q12): The average age of three children is 12 years. If the ages of two children are 18 and 12, find the third child’s age.
A) 4 years
B) 5 years
C) 6 years
D) 7 years
Answer: C) 6 years
Explanation:
- Step 1: Total age of 3 children = 12 × 3 = 36
- Step 2: Sum of two known ages = 18 + 12 = 30
- Step 3: Third child’s age = 36 − 30 = 6
- Final: Third child is 6 years, so option C is correct
Q13): The present ages of two brothers are in the ratio 7 : 9. If their age difference is 14 years, find the younger brother’s age.
A) 42 years
B) 45 years
C) 49 years
D) 51 years
Answer: C) 49 years
Explanation:
- Step 1: Let ages be 7k and 9k
- Step 2: Difference = 9k − 7k = 2k
- Step 3: Given 2k = 14 → k = 7
- Step 4: Younger’s age = 7k = 7 × 7 = 49
- Final: Younger is 49 years, so option C is correct
Q14): A man is 15 years older than his wife. 5 years ago, the man was twice as old as his wife. Find the wife’s present age.
A) 18 years
B) 20 years
C) 22 years
D) 24 years
Answer: B) 20 years
Explanation:
- Step 1: Let wife’s present age = w
- Step 2: Man’s present age = w + 15
- Step 3: 5 years ago: wife = w − 5, man = w + 10
- Step 4: Given w + 10 = 2(w − 5)
- Step 5: w + 10 = 2w − 10 → w = 20
- Final: Wife is 20 years, so option B is correct
Q15): A is 24 years old. After 6 years, the ratio of A’s age to B’s age becomes 5 : 4. Find B’s present age.
A) 16 years
B) 17 years
C) 18 years
D) 19 years
Answer: C) 18 years
Explanation:
- Step 1: A’s age after 6 years = 24 + 6 = 30
- Step 2: Let B’s present age = b → after 6 years = b + 6
- Step 3: Given (A after 6) : (B after 6) = 5 : 4
- Step 4: 30/(b + 6) = 5/4
- Step 5: 4 × 30 = 5(b + 6) → 120 = 5b + 30 → b = 18
- Final: B is 18 years, so option C is correct
Q16): A person’s present age is one-fourth of what it will be after 15 years. Find the present age.
A) 4 years
B) 5 years
C) 6 years
D) 8 years
Answer: B) 5 years
Explanation:
- Step 1: Let present age = x
- Step 2: Age after 15 years = x + 15
- Step 3: Given x = (1/4)(x + 15)
- Step 4: 4x = x + 15 → 3x = 15 → x = 5
- Final: Present age is 5 years, so option B is correct
Q17): The sum of ages of a father and mother is 70 years. Father is 6 years older than mother. Find the mother’s age.
A) 30 years
B) 31 years
C) 32 years
D) 34 years
Answer: C) 32 years
Explanation:
- Step 1: Let mother’s age = m
- Step 2: Father’s age = m + 6
- Step 3: Given m + (m + 6) = 70
- Step 4: 2m + 6 = 70 → 2m = 64 → m = 32
- Final: Mother is 32 years, so option C is correct
Q18): A is 4 years older than B. B is 10 years older than C. If A + C = 50, find B’s age.
A) 26 years
B) 27 years
C) 28 years
D) 29 years
Answer: C) 28 years
Explanation:
- Step 1: Let C’s age = c
- Step 2: Then B = c + 10
- Step 3: And A = B + 4 = (c + 10) + 4 = c + 14
- Step 4: Given A + C = 50 → (c + 14) + c = 50
- Step 5: 2c + 14 = 50 → 2c = 36 → c = 18
- Step 6: B = c + 10 = 18 + 10 = 28
- Final: B is 28 years, so option C is correct
Q19): Ten years ago, the ages of A and B were in the ratio 3 : 2. If their present age difference is 25 years, find A’s present age.
A) 80 years
B) 85 years
C) 90 years
D) 95 years
Answer: B) 85 years
Explanation:
- Step 1: Ten years ago, let ages be 3x and 2x
- Step 2: Their difference then = 3x − 2x = x
- Step 3: Difference in ages never changes, so present difference = x = 25
- Step 4: So x = 25 → ten years ago A = 3x = 75
- Step 5: Present age of A = 75 + 10 = 85
- Final: A is 85 years, so option B is correct
Q20): The sum of present ages of a father and his son is 66 years. After 6 years, father will be twice the son’s age. Find the son’s present age.
A) 18 years
B) 19 years
C) 20 years
D) 21 years
Answer: C) 20 years
Explanation:
- Step 1: Let son’s present age = s
- Step 2: Father’s present age = 66 − s
- Step 3: After 6 years: son = s + 6, father = 72 − s
- Step 4: Given (72 − s) = 2(s + 6)
- Step 5: 72 − s = 2s + 12 → 60 = 3s → s = 20
- Final: Son is 20 years, so option C is correct