Ages Ratio Calculation
Let the present ages of A and B be $5x$ and $3x$ respectively, according to the given ratio $5:3$.
Future Ages Ratio
After 5 years, their ages will be $(5x + 5)$ and $(3x + 5)$.
The problem states that the ratio of their ages after 5 years will be $10:7$. Therefore, we can set up the equation:
$ \frac{5x + 5}{3x + 5} = \frac{10}{7} $Solving for x
Cross-multiply to solve the equation:
$7(5x + 5) = 10(3x + 5)$
$35x + 35 = 30x + 50$
$35x - 30x = 50 - 35$
$5x = 15$
$x = \frac{15}{5}$
$x = 3$
Difference in Present Ages
Now, find the present ages:
- A's present age = $5x = 5 \times 3 = 15$ years
- B's present age = $3x = 3 \times 3 = 9$ years
The difference between their present ages is:
Difference = A's age - B's age = $15 - 9 = 6$ years.
Similar Questions
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Important Questions from Problems on Age
The age of Dr. Pandey is four times the age of his son. After 10 years, the age of Dr. Pandey will be twice the age of his son. The present age of Dr. Pandey's son is?
Three years ago, the average age of a family of six members was 19 years. Since then, a boy has been born, and the average age of the family is the same today as it was three years ago. What is the age of the boy?
Amita is 2 years older than her friend Amrita. Amita's father is twice as old as Amita, and Amrita is twice as old as her sister. The ages of Amita's father and Amrita's sister differ by 43 years. The sum of the ages (in years) of Amita and Amrita is:
- Narendra's mother is four times as old as Narendra. Four years ago, his mother was six times as old as Narendra was. What are their Present ages?
- A mother is now three times as old as her daughter. 5 years ago, she was four times as old as her daughter. What is the current age of the daughter?
