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?
8 : 9
Solving the Age Ratio Problem
This problem involves calculating the future age ratio of two individuals, A and B, based on their past age ratio and the sum of their current ages.
Representing Ages 6 Years Ago
We are given that the ratio between the ages of A and B 6 years ago was 5 : 6. We can represent their ages at that time using a variable, let's say $x$.
- Age of A 6 years ago = $5x$ years
- Age of B 6 years ago = $6x$ years
Calculating Present Ages
To find their present ages, we need to add 6 years to their ages from 6 years ago.
- A's present age = Age 6 years ago + 6 years = $5x + 6$ years
- B's present age = Age 6 years ago + 6 years = $6x + 6$ years
We are also given that the sum of their present ages is 45 years. We can set up an equation:
A's present age + B's present age = 45
$(5x + 6) + (6x + 6) = 45$
Now, we solve for $x$:
$11x + 12 = 45$
$11x = 45 - 12$
$11x = 33$
$x = \frac{33}{11}$
$x = 3$
Now we can find their present ages:
- A's present age = $5x + 6 = 5(3) + 6 = 15 + 6 = 21$ years
- B's present age = $6x + 6 = 6(3) + 6 = 18 + 6 = 24$ years
Let's check if the sum is correct: $21 + 24 = 45$. Yes, it matches the given information.
Determining Future Ages
The question asks for the ratio of their ages 3 years hence. This means we need to calculate their ages after 3 years from the present.
- A's age after 3 years = A's present age + 3 = $21 + 3 = 24$ years
- B's age after 3 years = B's present age + 3 = $24 + 3 = 27$ years
Finding the Final Ratio
Finally, we find the ratio of their ages 3 years from now.
Ratio = A's age after 3 years : B's age after 3 years
Ratio = $24 : 27$
To simplify the ratio, we find the greatest common divisor (GCD) of 24 and 27, which is 3.
Divide both numbers by 3:
$\frac{24}{3} = 8$
$\frac{27}{3} = 9$
So, the ratio of their ages 3 years hence will be $8 : 9$.
Similar Questions
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
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:
