Ratio and Proportion

Concept:In ratio problems, represent each term as a multiple of a common variable $k$ to find the actual values.Explanation:The given ratio $x:y:z = 2:3:5$ means that the quantities are in proportion to these numbers.Let the common multiplier be $k$.Then we have $x = 2k$, $y = 3k$, $z = 5k$.The sum $x+y+z$ is given as $60$.Substituting the expressions gives $2k + 3k + 5k = 60$.This simplifies to $10k = 60$.Solving for $k$, we divide both sides by $10$ to get $k = 6$.Now, $z$ is $5k$, so $z = 5 \times 6 = 30$.Thus, the value of $z$ is $30$.Answer:$z = 30$.