Average weight of three boys P,T and R is `54 (1)/(3)` kg. while the average weights of three boys T , F and G is 53 kg . What is the average weight of P,T,R,F and G ?

Options

A. 53.8 kg
B. 52.4 kg
C. 53.2 kg
D. cannot be determined

Answer

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

### Step 1: Calculate the total weight of boys P, T, and R.
The average weight of boys P, T, and R is given as \(54 \frac{1}{3}\) kg. We can convert this mixed number into an improper fraction:

\[ 54 \frac{1}{3} = \frac{54 \times 3 + 1}{3} = \frac{162 + 1}{3} = \frac{163}{3} \text{ kg} \]

To find the total weight of P, T, and R, we multiply the average by the number of boys (which is 3):

\[ \text{Total weight of P, T, R} = \frac{163}{3} \times 3 = 163 \text{ kg} \]

### Step 2: Calculate the total weight of boys T, F, and G.
The average weight of boys T, F, and G is given as \(53\) kg. To find the total weight, we multiply the average by the number of boys (which is 3):

\[ \text{Total weight of T, F, G} = 53 \times 3 = 159 \text{ kg} \]

### Step 3: Combine the total weights.
Now, we need to find the total weight of all five boys (P, T, R, F, and G). However, we notice that T is included in both groups. Therefore, we need to express the total weight of all five boys as follows:

\[ \text{Total weight of P, T, R, F, G} = (\text{Weight of P, T, R}) + (\text{Weight of T, F, G}) - \text{Weight of T} \]

Let’s denote the weight of T as \(T\). We can express the total weight as:

\[ \text{Total weight} = 163 + 159 - T \]

### Step 4: Calculate the average weight of P, T, R, F, and G.
To find the average weight of all five boys, we need to divide the total weight by 5:

\[ \text{Average weight} = \frac{(163 + 159 - T)}{5} \]

### Step 5: Conclusion.
Since we do not have the value of T, we cannot determine the exact average weight of P, T, R, F, and G. Therefore, the average weight cannot be determined with the information provided.

### Final Answer:
The average weight of P, T, R, F, and G cannot be determined.

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