Q1): The present ages of A and B differ by 6 years. After 4 years, their ages will be in the ratio 5 : 6. Find A’s present age.
A) 24 years
B) 25 years
C) 26 years
D) 27 years
Answer: C) 26 years
Explanation:
- Step 1: Let A’s present age = x, then B’s present age = x + 6
- Step 2: After 4 years: A = x + 4, B = x + 10
- Step 3: Given (x + 4) : (x + 10) = 5 : 6
- Step 4: 6(x + 4) = 5(x + 10)
- Step 5: 6x + 24 = 5x + 50 → x = 26
- Final: A’s present age is 26 years, so option C is correct
Q2): A father is 4 times as old as his son. After 10 years, the father will be 3 times as old as the son. Find the son’s present age.
A) 15 years
B) 18 years
C) 20 years
D) 22 years
Answer: C) 20 years
Explanation:
- Step 1: Let son’s present age = x
- Step 2: Father’s present age = 4x
- Step 3: After 10 years: father = 4x + 10, son = x + 10
- Step 4: Given 4x + 10 = 3(x + 10)
- Step 5: 4x + 10 = 3x + 30 → x = 20
- Final: Son’s present age is 20 years, so option C is correct
Q3): 5 years ago, the ages of A and B were in the ratio 2 : 3. If their present ages sum to 65 years, find B’s present age.
A) 36 years
B) 37 years
C) 38 years
D) 39 years
Answer: C) 38 years
Explanation:
- Step 1: 5 years ago, let ages be 2k and 3k
- Step 2: Present ages become (2k + 5) and (3k + 5)
- Step 3: Given (2k + 5) + (3k + 5) = 65
- Step 4: 5k + 10 = 65 → 5k = 55 → k = 11
- Step 5: B’s present age = 3k + 5 = 33 + 5 = 38
- Final: B is 38 years, so option C is correct
Q4): 5 years ago, a mother was 4 times as old as her daughter. After 15 years, the mother will be twice as old as the daughter. Find the daughter’s present age.
A) 13 years
B) 14 years
C) 15 years
D) 16 years
Answer: C) 15 years
Explanation:
- Step 1: Let daughter’s present age = d and mother’s present age = m
- Step 2: 5 years ago: m − 5 = 4(d − 5)
- Step 3: After 15 years: m + 15 = 2(d + 15)
- Step 4: From Step 2: m = 4d − 15
- Step 5: Put in Step 3: (4d − 15) + 15 = 2d + 30 → 4d = 2d + 30
- Step 6: 2d = 30 → d = 15
- Final: Daughter’s present age is 15 years, so option C is correct
Q5): The average age of 5 people is 28 years. If one person aged 32 is replaced by another aged 42, what is the new average age?
A) 29 years
B) 30 years
C) 31 years
D) 32 years
Answer: B) 30 years
Explanation:
- Step 1: Total age initially = 28 × 5 = 140
- Step 2: Remove 32 → new total = 140 − 32 = 108
- Step 3: Add 42 → new total = 108 + 42 = 150
- Step 4: New average = 150 ÷ 5 = 30
- Final: New average is 30 years, so option B is correct
Q6): A is 2 years older than B. B is 3 years younger than C. If A + B + C = 74, find B’s age.
A) 22 years
B) 23 years
C) 24 years
D) 25 years
Answer: B) 23 years
Explanation:
- Step 1: Let B’s age = b
- Step 2: Then A = b + 2
- Step 3: “B is 3 years younger than C” means C = b + 3
- Step 4: Sum: (b + 2) + b + (b + 3) = 74
- Step 5: 3b + 5 = 74 → 3b = 69 → b = 23
- Final: B is 23 years, so option B is correct
Q7): In 6 years, a person’s age will be ( \frac{5}{4} ) of his age 6 years ago. Find his present age.
A) 52 years
B) 54 years
C) 56 years
D) 58 years
Answer: B) 54 years
Explanation:
- Step 1: Let present age = x
- Step 2: Age after 6 years = x + 6
- Step 3: Age 6 years ago = x − 6
- Step 4: Given x + 6 = (5/4)(x − 6)
- Step 5: 4x + 24 = 5x − 30 → x = 54
- Final: Present age is 54 years, so option B is correct
Q8): The present ages of two sisters are in the ratio 5 : 7. After 6 years, their ages will be in the ratio 3 : 4. Find the younger sister’s present age.
A) 28 years
B) 30 years
C) 32 years
D) 34 years
Answer: B) 30 years
Explanation:
- Step 1: Let present ages be 5k and 7k
- Step 2: After 6 years: ages become (5k + 6) and (7k + 6)
- Step 3: Given (5k + 6)/(7k + 6) = 3/4
- Step 4: 4(5k + 6) = 3(7k + 6)
- Step 5: 20k + 24 = 21k + 18 → k = 6
- Step 6: Younger’s present age = 5k = 30
- Final: Younger sister is 30 years, so option B is correct
Q9): The sum of a father’s and son’s present ages is 68 years. 4 years ago, the father was 5 times the son’s age. Find the father’s present age.
A) 52 years
B) 53 years
C) 54 years
D) 55 years
Answer: C) 54 years
Explanation:
- Step 1: Let father’s present age = F and son’s present age = S
- Step 2: Given F + S = 68
- Step 3: 4 years ago: F − 4 = 5(S − 4)
- Step 4: F − 4 = 5S − 20 → F = 5S − 16
- Step 5: Substitute: (5S − 16) + S = 68 → 6S = 84 → S = 14
- Step 6: Father’s age = 68 − 14 = 54
- Final: Father is 54 years, so option C is correct
Q10): A’s age is ( \frac{2}{3} ) of B’s age. After 8 years, A’s age will be ( \frac{3}{4} ) of B’s age. Find A’s present age.
A) 14 years
B) 16 years
C) 18 years
D) 20 years
Answer: B) 16 years
Explanation:
- Step 1: Let A = 2k and B = 3k
- Step 2: After 8 years: A = 2k + 8, B = 3k + 8
- Step 3: Given (2k + 8)/(3k + 8) = 3/4
- Step 4: 4(2k + 8) = 3(3k + 8)
- Step 5: 8k + 32 = 9k + 24 → k = 8
- Step 6: A’s present age = 2k = 16
- Final: A is 16 years, so option B is correct
Q11): The present ages of A and B differ by 9 years. After 3 years, the sum of their ages will be 51 years. Find the older person’s present age.
A) 25 years
B) 26 years
C) 27 years
D) 28 years
Answer: C) 27 years
Explanation:
- Step 1: Let younger’s present age = y, older’s present age = y + 9
- Step 2: After 3 years: younger = y + 3, older = y + 12
- Step 3: Given (y + 3) + (y + 12) = 51
- Step 4: 2y + 15 = 51 → 2y = 36 → y = 18
- Step 5: Older’s present age = y + 9 = 27
- Final: Older person is 27 years, so option C is correct
Q12): The average age of 3 persons is 26 years. A fourth person joins, and the average becomes 25 years. Find the age of the fourth person.
A) 20 years
B) 21 years
C) 22 years
D) 23 years
Answer: C) 22 years
Explanation:
- Step 1: Total age of 3 persons = 26 × 3 = 78
- Step 2: Total age of 4 persons (new average 25) = 25 × 4 = 100
- Step 3: Age of fourth person = 100 − 78 = 22
- Final: Fourth person’s age is 22 years, so option C is correct
Q13): A man is 6 years older than his wife. 4 years ago, the man was 3 times as old as his wife. Find the wife’s present age.
A) 6 years
B) 7 years
C) 8 years
D) 9 years
Answer: B) 7 years
Explanation:
- Step 1: Let wife’s present age = w
- Step 2: Man’s present age = w + 6
- Step 3: 4 years ago: wife = w − 4, man = w + 2
- Step 4: Given w + 2 = 3(w − 4)
- Step 5: w + 2 = 3w − 12 → 2w = 14 → w = 7
- Final: Wife is 7 years, so option B is correct
Q14): The present ages of A and B are in the ratio 4 : 5. After 6 years, their ages will be in the ratio 5 : 6. Find A’s present age.
A) 20 years
B) 22 years
C) 24 years
D) 26 years
Answer: C) 24 years
Explanation:
- Step 1: Let present ages be A = 4k and B = 5k
- Step 2: After 6 years: A = 4k + 6, B = 5k + 6
- Step 3: Given (4k + 6)/(5k + 6) = 5/6
- Step 4: 6(4k + 6) = 5(5k + 6)
- Step 5: 24k + 36 = 25k + 30 → k = 6
- Step 6: A’s present age = 4k = 24
- Final: A is 24 years, so option C is correct
Q15): The older person is 12 years older than the younger. After 5 years, the older will be ( \frac{5}{3} ) of the younger. Find the younger person’s present age.
A) 12 years
B) 13 years
C) 14 years
D) 15 years
Answer: B) 13 years
Explanation:
- Step 1: Let younger’s present age = y
- Step 2: Older’s present age = y + 12
- Step 3: After 5 years: younger = y + 5, older = y + 17
- Step 4: Given y + 17 = (5/3)(y + 5)
- Step 5: 3y + 51 = 5y + 25 → 2y = 26 → y = 13
- Final: Younger person is 13 years, so option B is correct
Q16): 2 years ago, a boy was ( \frac{1}{3} ) of his father’s age. 4 years from now, the boy will be ( \frac{2}{5} ) of his father’s age. Find the boy’s present age.
A) 18 years
B) 19 years
C) 20 years
D) 21 years
Answer: C) 20 years
Explanation:
- Step 1: Let boy’s present age = x and father’s present age = y
- Step 2: 2 years ago: x − 2 = (1/3)(y − 2)
- Step 3: 4 years from now: x + 4 = (2/5)(y + 4)
- Step 4: Solve these two equations to get x = 20
- Step 5: (Quick check) 2 years ago: 18 is 1/3 of 54, correct
- Step 6: 4 years from now: 24 is 2/5 of 60, correct
- Final: Boy’s present age is 20 years, so option C is correct
Q17): A’s present age is 25% more than B’s present age. After 5 years, A will be 20% more than B. Find B’s present age.
A) 18 years
B) 20 years
C) 22 years
D) 24 years
Answer: B) 20 years
Explanation:
- Step 1: Let B’s present age = b
- Step 2: 25% more means A = 1.25b = 5b/4
- Step 3: After 5 years, 20% more means A + 5 = 1.2(B + 5) = 6(B + 5)/5
- Step 4: So (5b/4) + 5 = (6/5)(b + 5)
- Step 5: Multiply by 20: 25b + 100 = 24b + 120 → b = 20
- Final: B’s present age is 20 years, so option B is correct
Q18): The average age of 6 students is 18 years. A teacher joins them, and the average becomes 20 years. Find the teacher’s age.
A) 30 years
B) 31 years
C) 32 years
D) 33 years
Answer: C) 32 years
Explanation:
- Step 1: Total age of 6 students = 18 × 6 = 108
- Step 2: With teacher, total persons = 7 and average = 20
- Step 3: New total age = 20 × 7 = 140
- Step 4: Teacher’s age = 140 − 108 = 32
- Final: Teacher is 32 years, so option C is correct
Q19): A is 4 years less than 3 times B. After 5 years, A will be 2 times B. 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: Put A value: (3b − 4) + 5 = 2b + 10
- Step 5: 3b + 1 = 2b + 10 → b = 9
- Step 6: A = 3(9) − 4 = 23
- Final: A’s present age is 23 years, so option C is correct
Q20): The present ages of A, B, and C are in the ratio 2 : 3 : 5. After 4 years, the sum of their ages will be 62 years. Find C’s present age.
A) 20 years
B) 22 years
C) 24 years
D) 25 years
Answer: D) 25 years
Explanation:
- Step 1: Let present ages be 2k, 3k, and 5k
- Step 2: After 4 years, ages become 2k + 4, 3k + 4, 5k + 4
- Step 3: Sum after 4 years = (2k + 4) + (3k + 4) + (5k + 4)
- Step 4: 10k + 12 = 62 → 10k = 50 → k = 5
- Step 5: C’s present age = 5k = 25
- Final: C is 25 years, so option D is correct