p, q, r, s and t are five numbers such that the average of p. q and r is 5 and that of s and t is 10. What is the average of all the five numbers?
(a)7.75
(b)7.5
(c)7
(d)5

Options

A. 7.75
B. 7.5
C. 7
D. 5

Answer

To find the average of the five numbers \( p, q, r, s, \) and \( t \), we will follow these steps:

### Step 1: Calculate the sum of \( p, q, r \)
We know that the average of \( p, q, \) and \( r \) is 5. The formula for average is given by:

\[ \text{Average} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]

Here, the number of observations is 3 (since we have \( p, q, r \)). Therefore, we can express the sum of \( p, q, \) and \( r \) as:

\[ \frac{p + q + r}{3} = 5 \]

Multiplying both sides by 3 gives:

\[ p + q + r = 15 \]

### Step 2: Calculate the sum of \( s \) and \( t \)
Next, we know that the average of \( s \) and \( t \) is 10. Using the same formula for average, we have:

\[ \frac{s + t}{2} = 10 \]

Multiplying both sides by 2 gives:

\[ s + t = 20 \]

### Step 3: Calculate the total sum of all five numbers
Now, we can find the total sum of all five numbers \( p, q, r, s, \) and \( t \):

\[ p + q + r + s + t = (p + q + r) + (s + t) \]

Substituting the sums we calculated:

\[ p + q + r + s + t = 15 + 20 = 35 \]

### Step 4: Calculate the average of all five numbers
Finally, we can find the average of all five numbers:

\[ \text{Average} = \frac{p + q + r + s + t}{5} = \frac{35}{5} = 7 \]

Thus, the average of all five numbers is \( 7 \).

### Final Answer:
The average of all five numbers is \( 7 \), which corresponds to option (c).

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