Finding Z and P's Present Age Ratio

The question asks for the ratio of the present ages of Z and P. We are given information about their ages ten years ago.

Calculating Ages Ten Years Ago

• X's Age: Given as 5 years old ten years ago.
• Y's Age: Ten years ago, X's age (5) was half of Y's age. So, Y's age ten years ago was $2 \times 5 = 10$ years.
• Z's Age: Given as 18 years old ten years ago.
• P's Age: Ten years ago, Z (18) was 8 years younger than P. Therefore, P's age ten years ago was $18 + 8 = 26$ years.

Calculating Present Ages

To find the present ages, we add 10 years to their ages from ten years ago.

• Z's Present Age: $18 + 10 = 28$ years.
• P's Present Age: $26 + 10 = 36$ years.

Determining the Age Ratio

The ratio of the respective present ages of Z and P is calculated as:

Z's Present Age : P's Present Age

$28 : 36$

To simplify the ratio, find the greatest common divisor (GCD) of 28 and 36, which is 4.

Divide both numbers by 4:

$\frac{28}{4} : \frac{36}{4}$

$7 : 9$

The ratio of the respective ages of Z and P at present is 7:9.