AGE PROBLEMS
(a) 7 years
(b) 5 years
(c) 4 years
(d) 3 years
Answer-d
Let's assume the age of the son is x years.
According to the given information, the father is nine times as old as the son, so the father's age is 9x years.
The mother is eight times as old as the son, so the mother's age is 8x years.
The sum of the father's and the mother's age is 51 years:
9x + 8x = 51
17x = 51
x = 51 / 17
x = 3
Therefore, the age of the son is 3 years.
The correct answer is (d) 3 years.
Directions for the following 2 (two) items :
Read the following passage and answer the 2 (two) items that follow :
A, B, C, D, E and F are cousins. No two cousins are of the same age, but all have birthdays on the same day of the same month. The youngest is 17 years old and the oldest E is 22 years old. F is somewhere between B and D in age. A is older than B. C is older than D. A is one year older than C.
72. Which one of the following is possible? (2015)
(a) D is 20 years old
(b) F is 18 years old
(c) F is 19 years old
(d) F is 20 years old
Answer-b
Let's analyze the given information:
- The youngest cousin is 17 years old, and the oldest cousin E is 22 years old.
- F is somewhere between B and D in age.
- A is older than B.
- C is older than D.
- A is one year older than C.
Based on the given information, let's consider the possibilities:
(a) D is 20 years old: This is not possible because it contradicts the statement that C is older than D.
(b) F is 18 years old: This is possible since F can be between B and D in age, and it does not contradict any other given information.
(c) F is 19 years old: This is not possible since F cannot be older than E, who is already 22 years old.
(d) F is 20 years old: This is not possible since F cannot be older than E, who is already 22 years old.
Therefore, the only possible option is (b) F is 18 years old.
(a) 1
(b) 2
(c) 3
(d) 4
Answer-b
Based on the given conditions, the logically possible orders of the cousins in terms of increasing age are as follows:
1. E - A - C - B - F - D
2. E - A - C - D - F - B
Therefore, there are two logically possible orders of the cousins in terms of increasing age.
(a) 6 months
(b) 1 year
(c) 2 years
(d) 2 years and 6 months
Answer-b
The sum of the ages of 5 members 3 years ago = 80 years
Present age of 5 member = 80 + 3 × 5 = 95 years
The average age of 5 members 3 years ago = 80/5 = 16 years
Given the average age of 6 members at present is the same as the average age of 5 members 3 years ago
So the sum of 6 members (including baby) at present = 16*6 = 96 years
Age of baby = 96 - 95 = 1year
(a) 42
(b) 38
(c) 25
(d) 16
Answer-b
To solve this problem, we need to use the information given to find the current age of Mr X and then determine how long he must wait for his age to become a cube again.
Let us assume that Mr X's current age is "x". According to the problem statement, his age last year was a perfect square, so we can write:
(x-1) = a^2 ...eqn (1)
where "a" is some integer.
Also, his age next year will be a perfect cube, so we can write:
(x+1) = b^3 ...eqn (2)
where "b" is some integer.
We want to find the smallest possible value of "x" such that eqn (1) and eqn (2) are satisfied. Let's examine the cubes of the first few positive integers:
1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 64
If we set eqn (1) equal to eqn (2) and simplify, we get:
b^3 - a^2 = 2
We can see from the list of cubes that the only possible values for "a" and "b" are 5 and 3, respectively. Therefore, we have:
x - 1 = 5^2 = 25
x + 1 = 3^3 = 27
Solving for "x", we get x = 26.
To find out when Mr X's age will be a cube again, we simply need to find the next cube after 27, which is 64.
Therefore, he must wait 64 - 26 = 38 years. Thus, the answer is option (b) 38.
(a) 22 years
(b) 23 years
(c) 24 years
(d) 25 years
Answer-b
Let's break down the information given in the problem to solve it step by step:
- Ena is currently 13 years old.
- Ena's mother is 24 years older than Ena.
- Ena's mother is three years younger than Ena's father.
- Ena was born 4 years after her parent's marriage.
Let's assume that Ena's father got married at the age of "x" years. Based on the given information, we can calculate the ages of Ena's mother and Ena's father.
Ena's mother's age = Ena's age + 24 = 13 + 24 = 37 years
Ena's father's age = Ena's mother's age + 3 = 37 + 3 = 40 years
Now, we know that Ena was born 4 years after her parent's marriage. So, Ena's age + 4 = 13 + 4 = 17 years represents the duration of their marriage.
Therefore, Ena's father got married at the age of 40 - 17 = 23 years.
Hence, the answer is an option (b) 23 years.
(a) 25 years
(b) 30 years
(c) 35 years
(d) 45 years
Answer-c
Let's analyze the information given in the problem step by step to determine the age of the teacher:
The average age of a teacher and three students is 20 years. This implies that the sum of their ages is 20 multiplied by 4, which is 80 years.
Let's assume the age of each student is "x" years. Therefore, the age of the teacher would be "x + 20" years since the difference between the age of the teacher and each student is 20 years.
Since there are three students, their total age would be 3 multiplied by "x" years, which is 3x.
Now, we can set up an equation based on the given information:
(x + 20) + 3x = 80
Combining like terms, we get:
4x + 20 = 80
Subtracting 20 from both sides:
4x = 60
Dividing both sides by 4:
x = 15
So, the age of each student is 15 years. To find the age of the teacher, we add 20 to the age of each student:
Age of the teacher = 15 + 20 = 35 years
Therefore, the age of the teacher is 35 years, which corresponds to option (c).
Which of the above statements is/are correct? (2021)
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
Answer-b
Let us assume the present age of Y is y years.
So y years ago (the time when Y was born), the age of X is twice of Y's present age
⇒ Age of X, y years ago = 42 - y
So the equation becomes 42 - y = 2y ⇒ y = 14
So the present age of Y = 14 years
Statement 1: 8 years ago, the age of X was five times the age of Y.
According to the correct calculation, 8 years ago, the age of X would be 42 - 8 = 34 years, and the age of Y would be 14 - 8 = 6 years.
Is 34 equal to 5 times 6?
No, 34 is not equal to 5 times 6. Therefore, statement 1 is incorrect.
Statement 2: After 14 years, the age of X would be two times the age of Y.
After 14 years, the age of X would be 42 + 14 = 56 years, and the age of Y would be 14 + 14 = 28 years.
Is 56 equal to 2 times 28?
Yes, 56 is equal to 2 times 28. Therefore, statement 2 is correct.
In conclusion, only statement 2 is correct, so the answer is (b) 2 only.
