R got married 8 years ago. Her present age is$\frac{\mathrm{ 6}}{5}$ times her age at the time of her marriage. R’s brother was 10 years younger than her at the time of her marriage. What is the ratio of R's present age and her brother’s age at the time of her marriage?

Correct Option: 8:5

Let us solve this step-by-step to find the required ratio.

Step 1: Define the variables and set up the equation for R's age.
Let R's age at the time of her marriage be $x$ years.
Since R got married 8 years ago, her present age is ($x+8$) years.

According to the question, R's present age is $\frac{6}{5}$ times her age at the time of her marriage.

$x+8=\frac{6}{5}x$

Step 2: Solve for $x$ (R's age at marriage).
Multiply both sides of the equation by 5 to clear the fraction:

$5(x+8)=6x$

$5x+40=6x$

Subtract $5x$ from both sides:

$x=40$

So, R was 40 years old at the time of her marriage.

Step 3: Calculate R's present age and her brother's age at marriage.
R's present age = $x+8=40+8=48$ years.
R's brother was 10 years younger than her at the time of her marriage.
Brother's age at R's marriage = $40-10=30$ years.

Step 4: Find the required ratio.
Ratio of R's present age to her brother's age at the time of her marriage =

$\frac{48}{30}$

Dividing both the numerator and the denominator by 6 gives:

$\frac{8}{5}$

Therefore, the required ratio is 8:5.