Question

The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.
(a) 47.55 kg
(b) 48 kg
(c) 48.55 kg
(d) 49.25 kg

Answer 1

Hint: To solve this question, we will first calculate the total weight of 16 boys and that of 8 boys using the formula, \[\text{Average Weight}=\dfrac{\text{Total Weight}}{\text{Number of boys}}.\] After calculating the total weights of 16 and 8 boys, we will add them and again use the above stated formula to get the average weight.

Complete step by step answer:
Given that the average weight of 16 boys is 50.25 kg. The average weight can be determined by using the formula, \[\text{Average Weight}=\dfrac{\text{Total Weight}}{\text{Number of boys}}.\]
\[\Rightarrow \text{Average Weight of 16 boys}=\dfrac{\text{Total Weight of 16 boys}}{16}\]
Substituting the value of an average weight of 16 boys as 50.25 kg, we have,
\[\Rightarrow 50.25=\dfrac{\text{Total Weight of 16 boys}}{16}\]
\[\Rightarrow \text{Total Weight of 16 boys}=50.25\times 16\]
\[\Rightarrow \text{Total Weight of 16 boys}=804....\left( i \right)\]
Also, given that the average weight of 8 boys is 45.15 kg.
Following the similar process as above, we have,
\[\text{Average Weight of 8 boys}=\dfrac{\text{Total Weight of 8 boys}}{8}\]
Substituting the values we get,
\[\Rightarrow 45.15=\dfrac{\text{Total Weight of 8 boys}}{8}\]
\[\Rightarrow \text{Total Weight of 8 boys}=45.15\times 8\]
\[\Rightarrow \text{Total Weight of 8 boys}=361.2....\left( ii \right)\]
Adding equation (i) and (ii), we will get the total weight of all boys.
Therefore, total weight of all boys = Equation (i) + Equation (ii)
\[\Rightarrow \text{Total Weight of all boys}=804+361.2\]
\[\Rightarrow \text{Total Weight of all boys}=1165.2kg\]
Also, the total number of boys are 16 + 8 = 24.
Finally, we will calculate the average weight of all the boys using the above stated formula.
\[\Rightarrow \text{Average Weight of all boys}=\dfrac{\text{Total Weight}}{24}\]
\[\Rightarrow \text{Average Weight of all boys}=\dfrac{1165.2}{24}\]
\[\Rightarrow \text{Average Weight of all boys}=48.55\]
Therefore, the average weight of all the boys in the class is 48.55 kg.

So, the correct answer is “Option C”.

Note: A possibility of mistake can be directly adding the value of the average of 16 boys and the average of 8 boys and dividing it by 2 which is wrong because \[16\ne 8,16=2\times 8.\] Hence, dividing by 2 or 3 won’t work here. It is preferred to work with the above stated formula.