CBSE Class 10 Mathematics Problems on Ages MCQs Set 12

Mathematics Objective Questions and Answers: Problems on Ages

Access targeted multiple-choice questions for Problems on Ages designed to align with the latest CBSE academic syllabus for Class 10 Mathematics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

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View or download the dedicated Problems on Ages MCQ resource below. Practicing these 50 objective questions regularly builds familiarity with standard exam patterns and helps secure higher marks in final Mathematics evaluations.

Multiple Choice Questions

Question 1: The ages of A, B and C together total 185 years. B is twice as old as A and C is 17 years older than A. Then the respective ages of A, B and C are
(a) 40, 86 and 59 years
(b) 42, 84 and 59 years
(c) 40, 80 and 65 years
(d) None of these
Show Answer & Explanation

Answer: (b) 42, 84 and 59 years

Explanation:
1. Let A = x, B = 2x and C = x + 17: x + 2x + x + 17 = 185
2. 4x = 168, so A = 42, B = 84 and C = 59.

Teacher's Note:
1. Let the present ages be x and y and write each condition as an equation.
2. The difference between two ages never changes.

Question 2: If 1 is added to the age of the elder sister, then the ratio of the ages of the younger and the elder sister becomes 0.5 : 1, but if 2 is subtracted from the age of the younger one, the ratio of the younger to the elder becomes 1 : 3. Find the ages of the elder and the younger sister.
(a) 8 and 5
(b) 11 and 6
(c) 9 and 5
(d) 8 and 6
Show Answer & Explanation

Answer: (c) 9 and 5

Explanation:
1. Let the elder be E and the younger Y: Y/(E + 1) = 1/2 and (Y − 2)/E = 1/3
2. E = 2Y − 1 and 3Y − 6 = E, so 3Y − 6 = 2Y − 1 and Y = 5, E = 9
3. Check: 5/10 = 1/2 and 3/9 = 1/3.

Teacher's Note:
1. Let the present ages be x and y and write each condition as an equation.
2. The difference between two ages never changes.

Question 3: The age of the father 5 years ago was 5 times the age of his son. At present the father's age is 3 times that of his son. What is the present age of the father?
(a) 33 years
(b) 30 years
(c) 45 years
(d) None of these
Show Answer & Explanation

Answer: (b) 30 years

Explanation:
1. Let the son be s and the father 3s: 3s − 5 = 5(s − 5)
2. 3s − 5 = 5s − 25, so s = 10 and the father is 30 years old.

Teacher's Note:
1. Let the present ages be x and y and write each condition as an equation.
2. The difference between two ages never changes.

Question 4: Sonu is 4 years younger than Manu while Dolly is 4 years younger than Sumit and one-fifth times as old as Sonu. If Sumit is eight years old, how many times as old is Manu as Dolly?
(a) 6
(b) 1/2
(c) 3
(d) None of these
Show Answer & Explanation

Answer: (a) 6

Explanation:
1. Dolly = 8 − 4 = 4 years
2. Sonu = 5 × 4 = 20 years and Manu = 24 years
3. Manu/Dolly = 24/4 = 6.

Teacher's Note:
1. Let the present ages be x and y and write each condition as an equation.
2. The difference between two ages never changes.

Question 5: The age of a man is 3 times that of his son. 15 years ago, the man was 9 times as old as his son. What will be the age of the man after 15 years?
(a) 45 years
(b) 60 years
(c) 75 years
(d) 65 years
Show Answer & Explanation

Answer: (c) 75 years

Explanation:
1. Let the son be s and the man 3s: 3s − 15 = 9(s − 15)
2. 3s − 15 = 9s − 135, so s = 20 and the man is 60 now
3. After 15 years the man is 75 years old.

Teacher's Note:
1. Let the present ages be x and y and write each condition as an equation.
2. The difference between two ages never changes.

Question 6: Father is 5 years older than the mother and the mother's age now is thrice the age of the daughter. The daughter is now 10 years old. What was the father's age when the daughter was born?
(a) 20 years
(b) 15 years
(c) 25 years
(d) 30 years
Show Answer & Explanation

Answer: (c) 25 years

Explanation:
1. Mother = 3 × 10 = 30 years and father = 35 years now
2. When the daughter was born (10 years ago) the father was 35 − 10 = 25 years old.

Teacher's Note:
1. Let the present ages be x and y and write each condition as an equation.
2. The difference between two ages never changes.

Question 7: A father told his son, "I was as old as you are at present at the time of your birth". If the father is 38 years old now, then what was the son's age five years back?
(a) 14 years
(b) 19 years
(c) 38 years
(d) 33 years
Show Answer & Explanation

Answer: (a) 14 years

Explanation:
1. The father's age at the son's birth = the son's present age
2. So 38 − s = s, giving s = 19 years
3. Five years back the son was 14 years old.

Teacher's Note:
1. Let the present ages be x and y and write each condition as an equation.
2. The difference between two ages never changes.

Question 8: In a cricket team of 11, the average age of the 11 players is 28 years. Out of these, the average ages of three groups of three players each are 25 years, 28 years and 30 years respectively. If in these groups, the captain and the youngest player are not included and the captain is eleven years older than the youngest player, what is the age of the captain?
(a) 33 years
(b) 34 years
(c) 35 years
(d) 36 years
Show Answer & Explanation

Answer: (c) 35 years

Explanation:
1. Total age = 11 × 28 = 308
2. The three groups total 3(25 + 28 + 30) = 249, so the captain and youngest total 308 − 249 = 59
3. Let the youngest be y: y + (y + 11) = 59, so y = 24 and the captain is 35 years old.

Teacher's Note:
1. Let the present ages be x and y and write each condition as an equation.
2. The difference between two ages never changes.

Question 9: The average age of an adult class is 40 years. Twelve new students with an average age of 32 years join the class, thereby decreasing the average age of the class by 4 years. The original strength of the class was
(a) 10
(b) 11
(c) 12
(d) 15
Show Answer & Explanation

Answer: (c) 12

Explanation:
1. New average = 36 years
2. 40n + 12 × 32 = 36(n + 12)
3. 40n + 384 = 36n + 432, so 4n = 48 and n = 12.

Teacher's Note:
1. Let the present ages be x and y and write each condition as an equation.
2. The difference between two ages never changes.

Question 10: The present ages of Amit and his father are in the ratio of 2 : 5 respectively. Four years hence the ratio of their ages will become 5 : 11 respectively. What was the father's age five years ago?
(a) 40 years
(b) 45 years
(c) 30 years
(d) 35 years
Show Answer & Explanation

Answer: (d) 35 years

Explanation:
1. Let the ages be 2k and 5k: (2k + 4)/(5k + 4) = 5/11
2. 22k + 44 = 25k + 20, so k = 8 and the father is 40 now
3. Five years ago he was 35 years old.

Teacher's Note:
1. Let the present ages be x and y and write each condition as an equation.
2. The difference between two ages never changes.

Question 11: The respective ratio between the present age of Manisha and Deepali is 5 : x. Manisha is 9 years younger than Parineeta. Parineeta's age after 9 years will be 33 years. The difference between Deepali's and Manisha's age is the same as the present age of Parineeta. What will come in place of x?
(a) 23
(b) 39
(c) 15
(d) 13
Show Answer & Explanation

Answer: (d) 13

Explanation:
1. Parineeta is 33 − 9 = 24 now and Manisha is 24 − 9 = 15
2. Deepali = 15 + 24 = 39, so the ratio is 15 : 39 = 5 : 13
3. x = 13.

Teacher's Note:
1. Let the present ages be x and y and write each condition as an equation.
2. The difference between two ages never changes.

Question 12: The ages of Nishi and Vinnee are in the ratio of 6 : 5 respectively. After 9 years the ratio of their ages will be 9 : 8. What is the difference in their ages?
(a) 9 years
(b) 7 years
(c) 5 years
(d) 3 years
Show Answer & Explanation

Answer: (d) 3 years

Explanation:
1. (6k + 9)/(5k + 9) = 9/8, so 48k + 72 = 45k + 81 and k = 3
2. Ages are 18 and 15 years, so the difference = 3 years.

Teacher's Note:
1. Let the present ages be x and y and write each condition as an equation.
2. The difference between two ages never changes.

Question 13: The total of the ages of a class of 75 girls is 1050. The average age of 25 of them is 12 years and that of another 25 is 16 years. Find the average age of the remaining girls.
(a) 12 years
(b) 13 years
(c) 14 years
(d) 15 years
Show Answer & Explanation

Answer: (c) 14 years

Explanation:
1. Total of the remaining 25 = 1050 − 25 × 12 − 25 × 16 = 1050 − 300 − 400 = 350
2. Average = 350/25 = 14 years.

Teacher's Note:
1. Let the present ages be x and y and write each condition as an equation.
2. The difference between two ages never changes.

Question 14: Michelle got married 9 years ago. Today her age is 1 1/3 times her age at the time of marriage. At present her daughter's age is one-sixth of her age. What was her daughter's age two years ago?
(a) 6 years
(b) 7 years
(c) 3 years
(d) 4 years
Show Answer & Explanation

Answer: (d) 4 years

Explanation:
1. Let her age now be x: x = 4/3 (x − 9), so 3x = 4x − 36 and x = 36
2. Daughter's present age = 36/6 = 6, so two years ago she was 4 years old.

Teacher's Note:
1. Let the present ages be x and y and write each condition as an equation.
2. The difference between two ages never changes.

Question 15: Sneh's age is one-sixth of her father's age. Sneh's father's age will be twice of Vimal's age after 10 years. If Vimal's eighth birthday was celebrated 2 years before, then what is Sneh's present age?
(a) 30 years
(b) 24 years
(c) 6 years
(d) 5 years
Show Answer & Explanation

Answer: (d) 5 years

Explanation:
1. Vimal is 8 + 2 = 10 years old now and 20 after 10 years
2. Sneh's father will then be 40, so he is 30 now
3. Sneh = 30/6 = 5 years.

Teacher's Note:
1. Let the present ages be x and y and write each condition as an equation.
2. The difference between two ages never changes.

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FAQs

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Yes, our CBSE Class 10 Mathematics Problems on Ages MCQs Set 12 include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the CBSE paper is now competency-based.

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