The present age of Y is 28 years and four years hence the ratio of age of X to Y will be 7: 8. If present age of Z is 25% more than the present age of X, then find the age of Z six years ago?

The correct option is 24 years.

Let us break down the problem step-by-step to find the age of Z six years ago.

Step 1: Find Y's age four years from now
We are given that the present age of Y is 28 years.
Four years from now (hence), Y's age will be:
$\text{Age of Y four years hence}=28+4=32\text{years}$

Step 2: Find X's age four years from now
We are given that four years hence, the ratio of the age of X to Y will be 7 : 8.
Let the age of X four years hence be $X_{\text{future}}$.
Using the ratio:
$\frac{X_{\text{future}}}{32}=\frac{7}{8}$

Solving for $X_{\text{future}}$:
$X_{\text{future}}=32\times \frac{7}{8}$

$X_{\text{future}}=4\times 7=28\text{years}$

Step 3: Find the present age of X
Since X's age four years from now will be 28 years, X's present age is:
$\text{Present age of X}=28-4=24\text{years}$

Step 4: Find the present age of Z
We are given that the present age of Z is 25% more than the present age of X.
$\text{Present age of Z}=\text{Present age of X}+25\%\text{of Present age of X}$

$\text{Present age of Z}=24+(\frac{25}{100}\times 24)$

$\text{Present age of Z}=24+6=30\text{years}$

Step 5: Find the age of Z six years ago
Subtract 6 years from Z's present age:
$\text{Age of Z six years ago}=30-6=24\text{years}$