Two years ago the average age of P, Q, R and S was 30 years. On including A, the average present age of all five is 35 years. Then present age of A is
47 years
Understanding the Average Age Problem
This problem involves calculating the present age of a person, referred to as 'A', using information about the average ages of a group of people (P, Q, R, and S) at different times.
Calculating Past Total Age
We are given that the average age of four people (P, Q, R, S) two years ago was 30 years. To find the sum of their ages two years ago, we multiply the average age by the number of people:
Sum of ages of P, Q, R, S (two years ago) = Average age $\times$ Number of people
Sum of ages (two years ago) = $30 \times 4 = 120$ years.
Calculating Present Total Age of P, Q, R, S
Since the initial average was calculated two years ago, each of the four individuals (P, Q, R, S) is now 2 years older. Therefore, the total increase in their combined age is:
Increase in total age = Number of people $\times$ Number of years passed
Increase = $4 \times 2 = 8$ years.
Now, we can find the sum of the present ages of P, Q, R, and S:
Sum of present ages (P, Q, R, S) = Sum of ages (two years ago) + Increase in total age
Sum of present ages (P, Q, R, S) = $120 + 8 = 128$ years.
Calculating Present Total Age of P, Q, R, S, and A
When person A is included, the group size becomes 5 people. The problem states that the average present age of these five people (P, Q, R, S, A) is 35 years. The sum of their present ages is:
Sum of ages (P, Q, R, S, A, present) = Average present age $\times$ Number of people
Sum of ages (P, Q, R, S, A, present) = $35 \times 5 = 175$ years.
Determining the Present Age of A
To find the present age of person A, we subtract the sum of the present ages of P, Q, R, and S from the sum of the present ages of all five people (P, Q, R, S, A):
Present age of A = Sum of ages (P, Q, R, S, A, present) - Sum of present ages (P, Q, R, S)
Present age of A = $175 - 128 = 47$ years.
Conclusion
The present age of person A is 47 years.
Similar Questions
If 6 years ago the ratio between the ages of A and B was 5 : 6 and the sum of their ages at present is 45 years. what will be the ratio of their ages 3 years hence?
Important Questions from Problem on Age
The ratio of present ages of Neelam and Rajni is 6 : 7. After four years, their ages will be in the ratio of 8 : 9. What is the present age of Rajni?
Five years ago the age of the son was one third of that of his mother at that time. If the sum of their present ages is 70 years, then find the present age of the mother.
Jaya is 36 years old and her son Bharat is 11 years old. In how many years will Jaya be twice as Bharat's age?
Five years ago, father's age was 5 times that of his son and after 3 years he will be 3 times as old as his son. Find the present age of son.
The ratio of a father's age to his son's age is 3 ∶ 2 The product of the numbers representing their age is 486. The ratio of their ages after 5 years will be:
