Question
The ages of A and B are in the ratio of 5 : 3. After 5 years the ratio of their ages will be 10 : 7. What is the difference between present ages of A and B(in years)?
This question was previously asked in
RRB NTPC 2019 CBT 1 Question Paper PDF (31-Jan-2021) (Shift 1)
The correct answer is
6
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.
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