Problems Based On Age

Explanation
The question states that the sum of the ages of a son and father is 56 years, and the age of the father will be three times that of the son. Let's assume the age of the son is x. According to the given information, the age of the father will be 3x. Therefore, the equation becomes x + 3x = 56. Simplifying this equation, we get 4x = 56. Dividing both sides by 4, we find that x = 14. Therefore, the age of the son is 14 years.

Explanation
The correct answer is 10 years. This can be determined by setting up a proportion based on the given ratios. The current ratio of the father's age to the son's age is 6:1, and the ratio after 5 years is 7:2. By setting up the proportion (6+x)/(1+x) = 7/2, where x represents the number of years after 5 years, we can solve for x. Simplifying this equation gives us 12+2x = 7+7x. Solving for x gives us x=5. Therefore, the son's current age is 5 years, which means that after 5 years, he will be 10 years old.

Explanation
Five years ago, the man's age was nine times the age of his son at that time. Let's assume the son's age five years ago was x. So, the man's age five years ago would be 9x. Currently, the man's age is four times that of his son, which means the man's age is 4x. To find the present age of the man, we need to add 5 years to his age five years ago, which gives us 9x + 5. Since 9x + 5 is equal to 4x (the man's current age), we can solve for x. By solving the equation, we find that x = 5. Therefore, the present age of the man is 4x = 4 * 5 = 20. Adding 5 years to his current age gives us the answer of 25 years.

Explanation
Let's assume the present age of the daughter is x years. Then, the present age of the mother would be 50 - x years.
According to the given information, 5 years ago, the mother's age was 7 times the age of the daughter.
So, (50 - x) - 5 = 7(x - 5).
Simplifying this equation, we get 45 - x = 7x - 35.
Bringing like terms together, we have 8x = 80.
Dividing both sides by 8, we find x = 10.
Therefore, the present age of the daughter is 10 years and the present age of the mother is 50 - 10 = 40 years.

Explanation
The given information states that the ratio of the father's age to the son's age is 6:1. This means that for every 6 years the father ages, the son ages 1 year. The product of their ages is 216, which means that the father's age multiplied by the son's age equals 216. To find the individual ages, we can divide 216 by 7 (6+1). This gives us 31 for the father's age and 5 for the son's age. After six years, the father will be 37 and the son will be 11. Therefore, the ratio of their ages after six years will be 7:2.

Explanation
Let's assume the present age of the younger person is x years. Since the difference between their ages is 10 years, the present age of the elder person would be x+10 years.

Now, we are given that !% years ago, the elder one was twice as old as the younger one. So, !% years ago, the younger person's age would have been x-!% years and the elder person's age would have been (x+10)-!% years.

According to the given information, (x+10)-!% = 2(x-!%).

Simplifying this equation, we get x = !%, which means the present age of the younger person is !% years.

Therefore, the present age of the elder person would be !%+10 years, which is 35 years.

Explanation
Pushpa is twice as old as Rita was two years ago. Let's assume Rita's age two years ago was x. Therefore, Pushpa's age two years ago would be 2x.

According to the given information, the difference between their ages is two years. So, we can write the equation as 2x - x = 2. Solving this equation, we get x = 2.

Since Rita's age two years ago was 2, her current age would be 2 + 2 = 4.

Pushpa's age is twice as old as Rita's age two years ago, which means Pushpa's age is 2 * 2 = 4.

Therefore, Pushpa is 8 years old today.

Explanation
After 5 years, the age of the father will be thrice the age of his son. This implies that the father's age will be three times the son's age plus 5.

Five years ago, the father was seven times as old as his son. This implies that the father's age five years ago was seven times the son's age minus 5.

To solve this problem, we can set up two equations:

1) Father's age + 5 = 3 * (Son's age + 5)
2) Father's age - 5 = 7 * (Son's age - 5)

By solving these equations simultaneously, we can find that the father's age is 40 years.

Explanation
Five years ago, Atul was 1/4th as old as his uncle, which means that Atul's age was 1/4th of his uncle's age minus 5 years. Let's assume the uncle's age 5 years ago was U. So, Atul's age 5 years ago would be U/4 - 5. Currently, Atul is 30 years younger than his uncle, so Atul's current age would be U - 30. Equating these two expressions, we get U - 30 = U/4 - 5. Solving this equation, we find U = 80. Therefore, Atul's uncle is currently 80 years old. In 5 years, his age will be 80 + 5 = 85.