The average weight of three boys P, Q and R is 54 kg, while the average weight of three boys Q, S and T is 60 kg. What is the average weight of P, Q, R, S and T?

Options

A. a. 66.4 kg
B. b. 63.2 kg
C. c. 58.8 kg
D. d. data insufficient

Answer

To solve the problem step by step, we will first calculate the total weights of the groups of boys and then find the average weight of all five boys.

### Step 1: Calculate the total weight of boys P, Q, and R

The average weight of boys P, Q, and R is given as 54 kg. The formula for average is:

\[ \text{Average} = \frac{\text{Total Weight}}{\text{Number of Boys}} \]

Using this formula, we can find the total weight of P, Q, and R:

\[ \text{Total Weight of P, Q, R} = \text{Average} \times \text{Number of Boys} = 54 \, \text{kg} \times 3 = 162 \, \text{kg} \]

### Step 2: Calculate the total weight of boys Q, S, and T

The average weight of boys Q, S, and T is given as 60 kg. Using the same formula:

\[ \text{Total Weight of Q, S, T} = \text{Average} \times \text{Number of Boys} = 60 \, \text{kg} \times 3 = 180 \, \text{kg} \]

### Step 3: Combine the total weights

Now, we can add the total weights of the two groups:

\[ \text{Total Weight of P, Q, R} + \text{Total Weight of Q, S, T} = 162 \, \text{kg} + 180 \, \text{kg} = 342 \, \text{kg} \]

### Step 4: Express the combined total weight

From the total weights, we can express it in terms of individual weights:

\[ P + Q + R + Q + S + T = P + 2Q + R + S + T = 342 \, \text{kg} \]

### Step 5: Calculate the average weight of P, Q, R, S, and T

To find the average weight of all five boys (P, Q, R, S, and T), we need to divide the total weight by the number of boys:

\[ \text{Average Weight of P, Q, R, S, T} = \frac{P + 2Q + R + S + T}{5} \]

However, we cannot find the average directly because we have 2Q in the equation and we do not know the value of Q. Therefore, we cannot determine the average weight of P, Q, R, S, and T without knowing the weight of Q.

### Conclusion

Since we do not have enough information to determine the average weight of all five boys, the answer is:

**Data Insufficient**

---