The average of a, 11, 23, 17 is 15 and the average of a,b,12, 25 is 16. The value of `(a)/(b)` is :

Options

A. `1/3`
B. `1/2`
C. `2/3`
D. `3/4`

Answer

To solve the problem step by step, we will first find the value of \( a \) and then \( b \) using the given averages.

### Step 1: Find the value of \( a \)

The average of the numbers \( a, 11, 23, 17 \) is given as 15.

The formula for average is:
\[ \text{Average} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]

For our case:
\[ 15 = \frac{a + 11 + 23 + 17}{4} \]

Now, we can calculate the sum of the observations:
\[ a + 11 + 23 + 17 = 15 \times 4 \]
\[ a + 51 = 60 \]

Now, isolate \( a \):
\[ a = 60 - 51 \]
\[ a = 9 \]

### Step 2: Find the value of \( b \)

Next, we use the second average given for the numbers \( a, b, 12, 25 \) which is 16.

Using the same average formula:
\[ 16 = \frac{a + b + 12 + 25}{4} \]

Substituting the value of \( a \):
\[ 16 = \frac{9 + b + 12 + 25}{4} \]

Calculating the sum:
\[ 9 + b + 37 = 16 \times 4 \]
\[ 9 + b + 37 = 64 \]

Now, isolate \( b \):
\[ b + 46 = 64 \]
\[ b = 64 - 46 \]
\[ b = 18 \]

### Step 3: Find the value of \( \frac{a}{b} \)

Now that we have both \( a \) and \( b \):
\[ a = 9, \quad b = 18 \]

We can find \( \frac{a}{b} \):
\[ \frac{a}{b} = \frac{9}{18} = \frac{1}{2} \]

Thus, the final answer is:
\[ \frac{a}{b} = \frac{1}{2} \]