There are two sections A and B of a class, consisting of 18 and 22 students, respectively. If the average weig

Question

There are two sections A and B of a class, consisting of 18 and 22 students, respectively. If the average weight of section A is $ 40 	ext{ kg}$ and that of section B is $ 35 	ext{ kg}$, find the average weight of the whole class.

Examoogle · Accepted Answer

The correct answer is Option B: 37.25 kg. Use the weighted average formula directly: $	ext{Avg} = \frac{18 	imes 40 + 22 	imes 35}{18 + 22} = \frac{720 + 770}{40} = \frac{1490}{40} = 37.25$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Use the weighted average formula directly: $	ext{Avg} = \frac{18 	imes 40 + 22 	imes 35}{18 + 22} = \frac{720 + 770}{40} = \frac{1490}{40} = 37.25$.

Formula Used: $$	ext{Average} = \frac{\sum 	ext{Values}}{	ext{Total Number of Values}} = \frac{n_1 A_1 + n_2 A_2}{n_1 + n_2}$$

Given: Number of students in section A = 18, Average weight = 40 kg. Number of students in section B = 22, Average weight = 35 kg.

Steps: Calculate total weight for Section A: Multiply the number of students by their average weight: $18 	imes 40$.. Calculate total weight for Section B: Multiply the number of students by their average weight: $22 	imes 35$.. Find the average weight of the whole class: Divide the total sum of weights by the total number of students ($18 + 22 = 40$): $\frac{720 + 770}{40}$.

Answer: B is correct because the weighted average calculation $1490 \div 40$ results in $37.25 	ext{ kg}$.

Exam Tip: This concept is fundamental for 'Alligation and Mixture' problems in Quantitative Aptitude, where the ratio of quantities acts as the weight.

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