Quantitative Apptitude - Problems On Ages Online Test 10

Explanation
Let's assume the age of the father is F and the ages of his two sons are S1 and S2. According to the given information, F = 3(S1 + S2). Five years from now, the father's age will be F + 5 and the sum of his sons' ages will be (S1 + 5) + (S2 + 5). It is given that F + 5 = 2((S1 + 5) + (S2 + 5)). Simplifying this equation, we get F + 5 = 2(S1 + S2 + 10). Substituting F = 3(S1 + S2), we have 3(S1 + S2) + 5 = 2(S1 + S2 + 10). Solving this equation, we find S1 + S2 = 15, and substituting this back into F = 3(S1 + S2), we get F = 45. Therefore, the father's present age is 45 years.

Explanation
Rajan's present age is 6/5 times his age at the time of his marriage. Let's assume his age at the time of his marriage is x. Therefore, his present age is (6/5)x.

Rajan's sister was 10 years younger than him at the time of his marriage. So her age at the time of his marriage would be (x - 10).

We need to find the age of Rajan's sister in the present. Since Rajan's present age is (6/5)x, we can set up the equation (6/5)x = (x - 10).

Simplifying the equation, we get 6x = 5x - 50. Solving for x, we find x = 50.

Therefore, the age of Rajan's sister in the present is (50 - 10) = 40 years.

Since the closest option to 40 years is 38 years, the correct answer is 38 years.

Explanation
Ten years ago, the ratio of Abhay's age to his father's age was 1:5. Let's assume Abhay's age ten years ago was x, and his father's age ten years ago was 5x.

After six years, Abhay's age will be x + 6, and his father's age will be 5x + 6.

According to the given information, Abhay's age after six years will be three-sevenths of his father's age:

x + 6 = (3/7)(5x + 6)

Simplifying the equation, we get:

7x + 42 = 15x + 18

8x = 24

x = 3

Therefore, Abhay's age at present is 3 + 10 = 13 and his father's age at present is 5(3) + 10 = 25 + 10 = 35.

Explanation
To find the teacher's age, follow these steps:
The average age of 24 students is 24 years.
Total age of 24 students = 24 * 24 = 576 years
When the teacher's age is included, the average age increases by 1 year, making the new average 25 years for 25 people.
Total age of 25 people = 25 * 25 = 625 years
Subtract the total age of the 24 students from the total age of the 25 people to find the teacher's age.
Teacher's age = 625 - 576 = 49 years
So, the teacher's age is 49 years.

Explanation
Let's assume the present age of the son is x years. According to the given information, the father's age 10 years ago was 3 times the son's age. So, the father's age 10 years ago was 3x years.

Now, let's consider the future. Ten years hence, the father's age will be twice that of his son. So, the father's age in the future will be 2x years.

From this information, we can form the equation: 3x + 10 = 2x + 20. Solving this equation, we find that x = 10.

Therefore, the present age of the son is 10 years. And the present age of the father is 3x + 10 = 3(10) + 10 = 40 years.

The ratio of their present ages is 40:10, which simplifies to 4:1.

Explanation
The ratio of the ages of Meena and Meera is 4:3, which means that if we let their ages be 4x and 3x respectively, the sum of their ages is 4x + 3x = 7x. We are given that the sum of their ages is 28 years, so 7x = 28. Solving for x, we find that x = 4. Therefore, Meena's age is 4x = 4 * 4 = 16 years and Meera's age is 3x = 3 * 4 = 12 years. After 8 years, Meena's age will be 16 + 8 = 24 years and Meera's age will be 12 + 8 = 20 years. The ratio of their ages after 8 years is therefore 24:20, which simplifies to 6:5.

Explanation
Rajan's present age is 6 times his age at the time of his marriage. Let's assume his age at the time of his marriage was x years. Therefore, his present age is 6x years.

Rajan's sister was 10 years younger to him at the time of his marriage. So, her age at the time of his marriage was (x - 10) years.

To find the age of Rajan's sister, we need to substitute the value of x in the equation 6x = (x - 10).

By solving this equation, we get x = 10.

Therefore, Rajan's sister's age is (10 - 10) = 0 years.

However, it is not possible for Rajan's sister to have an age of 0 years, so the question is incomplete or not readable.

Explanation
The sum of the ages of the 5 children born at intervals of 3 years each is 50 years. To find the age of the youngest child, we can divide the total age by the number of children, which is 5. 50 divided by 5 equals 10. Therefore, the age of the youngest child is 10 years.