If U : V = 2 : 9, V : W = 3 : 5 and W : X = 15: 11, then what is the value of U : X?

Options

A. `3 : 22`
B. `4 :17`
C. `2 : 11`
D. `5 : 11`

Answer

To find the value of the ratio \( U : X \) given the ratios \( U : V = 2 : 9 \), \( V : W = 3 : 5 \), and \( W : X = 15 : 11 \), we can follow these steps:

### Step 1: Express each ratio in terms of a common variable
Let’s denote:
- \( U = 2k \) (from \( U : V = 2 : 9 \))
- \( V = 9k \)

### Step 2: Use the second ratio to express W in terms of V
From \( V : W = 3 : 5 \):
- Since \( V = 9k \), we can express \( W \) as follows:
\[ \frac{V}{W} = \frac{3}{5} \implies W = \frac{5}{3} V = \frac{5}{3} (9k) = 15k \]

### Step 3: Use the third ratio to express X in terms of W
From \( W : X = 15 : 11 \):
- Since \( W = 15k \), we can express \( X \) as follows:
\[ \frac{W}{X} = \frac{15}{11} \implies X = \frac{11}{15} W = \frac{11}{15} (15k) = 11k \]

### Step 4: Now we have expressions for U and X
- \( U = 2k \)
- \( X = 11k \)

### Step 5: Find the ratio \( U : X \)
Now we can find the ratio \( U : X \):
\[ U : X = 2k : 11k = 2 : 11 \]

### Final Answer
Thus, the value of \( U : X \) is \( 2 : 11 \).

---