If x% of y is 150 and y% of z is 300, then the relation between x and z is:
(a)z = x
(b)`z=x//3`
(c)`z=x//2`
(d)`z=2x`

Options

A. z = x
B. `z=x//3`
C. `z=x//2`
D. `z=2x`

Answer

To solve the problem step by step, we need to analyze the given information and derive the relationship between \( x \) and \( z \).

### Step 1: Set up the equations based on the given information
We know that:
1. \( x\% \) of \( y \) is 150.
2. \( y\% \) of \( z \) is 300.

From the first statement, we can express it mathematically as:
\[ \frac{x}{100} \cdot y = 150 \]
From the second statement, we can express it as:
\[ \frac{y}{100} \cdot z = 300 \]

### Step 2: Rearranging the equations
From the first equation, we can solve for \( y \):
\[ y = \frac{150 \cdot 100}{x} = \frac{15000}{x} \]

From the second equation, we can solve for \( y \):
\[ y = \frac{300 \cdot 100}{z} = \frac{30000}{z} \]

### Step 3: Equate the two expressions for \( y \)
Now we have two expressions for \( y \):
\[ \frac{15000}{x} = \frac{30000}{z} \]

### Step 4: Cross-multiply to eliminate the fractions
Cross-multiplying gives us:
\[ 15000z = 30000x \]

### Step 5: Simplify the equation
Dividing both sides by 15000:
\[ z = \frac{30000}{15000}x \]
\[ z = 2x \]

### Conclusion
Thus, the relationship between \( x \) and \( z \) is:
\[ z = 2x \]

The correct answer is (d) \( z = 2x \).

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