A is 44 years old and B is 19 years old. After how many years will A be twice as old as B?
Solution
44 + x = 2(19 + x) ⇒ x = 44 − 38 = 6.
Answer: (A) 6 years
Quantitative Aptitude · Arithmetic
Problems on Ages: MAH CET, NMAT and SNAP practice questions
20 questions in the pattern of MAH MBA CET, NMAT and SNAP. Each question is marked with the exams it suits. Answer it, then open the step-by-step solution.
Exam:
A's father was 27 years old when A was born, and A's mother was 23 years old when A's brother, who is 6 years younger than A, was born. What is the difference between the parents' ages?
Solution
When A was born, the mother was 23 − 6 = 17 years old.
Difference = 27 − 17 = 10 years.
Answer: (D) 10 years
The ratio of A's and B's ages is 3 : 5. 8 years from now, the sum of their ages will be 64. What is B's present age?
Solution
Present sum = 64 − 16 = 48.
B = 5/8 × 48 = 30.
Answer: (A) 30 years
9 years ago, the ages of A and B were in the ratio 2 : 5. A is now 23 years old. How old is B now?
Solution
9 years ago A was 14 = 2k, so k = 7.
B then = 35; now 44.
Answer: (D) 44 years
The present ages of A and B are in the ratio 5 : 7. After 12 years the ratio will be 4 : 5. What is A's present age?
Solution
(5k + 12) : (7k + 12) = 4 : 5.
5(5k + 12) = 4(7k + 12) gives k = 4; A = 20.
Answer: (A) 20 years
The average age of a mother and her 5 children is 20 years. The average age of the children is 12 years. What is the mother's age?
Solution
Total = 6 × 20 = 120; children total 5 × 12 = 60.
Mother = 60 years.
Answer: (B) 60 years
The average age of a mother and her 4 children is 21 years. The average age of the children is 16 years. What is the mother's age?
Solution
Total = 5 × 21 = 105; children total 4 × 16 = 64.
Mother = 41 years.
Answer: (D) 41 years
The ages of two sisters are in the ratio 4 : 7 and differ by 27 years. What is the age of the elder sister?
Solution
Difference = 3 parts = 27, so one part = 9.
Elder = 7 × 9 = 63.
Answer: (B) 63 years
B is 4 years older than A, and C is 3 years older than B. The sum of their ages is 101. How old is C?
Solution
A = x, B = x + 4, C = x + 7. Sum = 3x + 11 = 101.
x = 30, so C = 37.
Answer: (A) 37 years
10 years ago, the ages of A and B were in the ratio 7 : 3. A is now 66 years old. How old is B now?
Solution
10 years ago A was 56 = 7k, so k = 8.
B then = 24; now 34.
Answer: (D) 34 years
A's father was 28 years old when A was born, and A's mother was 25 years old when A's brother, who is 2 years younger than A, was born. What is the difference between the parents' ages?
Solution
When A was born, the mother was 25 − 2 = 23 years old.
Difference = 28 − 23 = 5 years.
Answer: (D) 5 years
The ages of two children differ by 4 years, and the product of their ages is 60. What is the age of the elder child?
Solution
x(x + 4) = 60.
x = 6 works (6 × 10 = 60), so the elder is 10.
Answer: (A) 10 years
B is 8 years older than A, and C is 3 years older than B. The sum of their ages is 58. How old is C?
Solution
A = x, B = x + 8, C = x + 11. Sum = 3x + 19 = 58.
x = 13, so C = 24.
Answer: (D) 24 years
The present ages of A and B are in the ratio 7 : 2. After 8 years the ratio will be 8 : 3. What is A's present age?
Solution
(7k + 8) : (2k + 8) = 8 : 3.
3(7k + 8) = 8(2k + 8) gives k = 8; A = 56.
Answer: (D) 56 years
A father is 5 times as old as his son. After 15 years he will be 3 times as old as his son. What is the son's present age?
Solution
Let the son be s: 5s + 15 = 3(s + 15).
Solving gives s = 15.
Answer: (C) 15 years
The ages of two children differ by 6 years, and the product of their ages is 160. What is the age of the elder child?
Solution
x(x + 6) = 160.
x = 10 works (10 × 16 = 160), so the elder is 16.
Answer: (D) 16 years
The ages of two sisters are in the ratio 4 : 5 and differ by 8 years. What is the age of the elder sister?
Solution
Difference = 1 part = 8, so one part = 8.
Elder = 5 × 8 = 40.
Answer: (C) 40 years
A is 46 years old and B is 17 years old. After how many years will A be twice as old as B?
Solution
46 + x = 2(17 + x) ⇒ x = 46 − 34 = 12.
Answer: (B) 12 years
The sum of the ages of a father and son is 54 years. After 3 years the father will be 5 times as old as the son. What is the father's present age?
Solution
Son = s, father = 54 − s. (54 − s + 3) = 5(s + 3).
Solving gives s = 7, so the father is 47.
Answer: (D) 47 years
The ratio of A's and B's ages is 2 : 7. 5 years from now, the sum of their ages will be 46. What is B's present age?
Solution
Present sum = 46 − 10 = 36.
B = 7/9 × 36 = 28.
Answer: (D) 28 years
These are original practice questions written by Target Campus in the pattern and difficulty of MAH MBA CET, NMAT, SNAP and other MBA entrance tests. They are not previous-year papers.
Preparing for MAH CET, NMAT, SNAP or CAT? Courses, live classes and mocks by Dr. Kiran Derle at Target Campus.
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