Ages Calculation: Understanding the Problem
This problem involves calculating the present age of Ravi based on information about the average ages of his family members at different points in the past. We need to set up equations based on the given averages and solve them systematically.
Ages Six Years Ago
Let R, W, and C represent the present ages of Ravi, his wife, and their child, respectively.
According to the question, six years ago, the average age of Ravi, his wife, and their child was 32 years.
The ages of Ravi, his wife, and child six years ago were $(R-6)$, $(W-6)$, and $(C-6)$.
The sum of their ages six years ago can be calculated as:
Sum of ages (6 years ago) = Average age $\times$ Number of people
Sum of ages (6 years ago) = $32 \times 3 = 96$
So, we can write the equation:
$$ (R-6) + (W-6) + (C-6) = 96 $$Simplifying this equation:
$$ R + W + C - 18 = 96 $$Adding 18 to both sides gives the sum of their present ages:
$$ R + W + C = 96 + 18 $$ $$ R + W + C = 114 \quad \quad (1) $$Ages Nine Years Ago
Next, the question states that nine years ago, the average age of Ravi's wife and the child was 24 years.
The ages of Ravi's wife and child nine years ago were $(W-9)$ and $(C-9)$.
The sum of their ages nine years ago is:
Sum of ages (wife & child, 9 years ago) = Average age $\times$ Number of people
Sum of ages (wife & child, 9 years ago) = $24 \times 2 = 48$
This gives us the equation:
$$ (W-9) + (C-9) = 48 $$Simplifying this equation:
$$ W + C - 18 = 48 $$Adding 18 to both sides gives the sum of the present ages of the wife and child:
$$ W + C = 48 + 18 $$ $$ W + C = 66 \quad \quad (2) $$Finding Ravi's Present Age
Now we have two equations:
- Equation (1): $R + W + C = 114$
- Equation (2): $W + C = 66$
We can find Ravi's present age (R) by substituting the value of $(W+C)$ from Equation (2) into Equation (1).
Substituting $(W+C)$ in Equation (1):
$$ R + (66) = 114 $$To find R, subtract 66 from both sides:
$$ R = 114 - 66 $$ $$ R = 48 $$Therefore, Ravi's present age is 48 years.
Similar Questions
- The average age of 4 members of a family is 35 years. Their ages are in the ratio 8:7:1:12. What is the age of the oldest member of the family (in years)?
- Four years ago, the ratio of the ages of A and B was 3: 5. Six years hence, the ratio of the ages of A and B will be 2: 3. What is the sum (in years) of the present ages of A and B?
The ages of A and B are in the ratio 4: 7, respectively. After 8 years, the ratio of their ages will be 2: 3. What is the sum of the ages of A and B (in years)?
The present ages of Ramu and Ravi are in the ratio of 4: 3. After 5 years the ratio of their ages will be 5: 4. Find their present ages, respectively.
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?
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:
X said to Y, "At the time of your birth I was twice as old as you are at present." If the present age of X is 42 years, then consider the following statements:
1. 8 years ago, the age of X was five times the age of Y.
2. After 14 years, the age of X would be two times the age of Y.
Which of the above statements is/are correct?
