d Problem 4: The average weight of a group of boys and girls is 38 kgs. The average weight of the boys is 42 kgs, and that of girls is 33 kgs. If the number of boys is 25. find the number of girls. | Job Exam Rare Mathematics (JEMrare) - Solved MCQs
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Problem 4: The average weight of a group of boys and girls is 38 kgs. The average weight of the boys is 42 kgs, and that of girls is 33 kgs. If the number of boys is 25. find the number of girls.

Problem 4: The average weight of a group of boys and girls is 38 kgs. The average weight of the boys is 42 kgs, and that of girls is 33 kgs. If the number of boys is 25. find the number of girls.

a) 10              b) 20             c) 15                 d) 17

Solution:

Let the weight of 25 boys be w1,w2,w3,…………w25. Their average weight is 42kg

\Rightarrow \frac{w1+w2+w3+......+w25}{25}=42

Now suppose total weight of boys  w1+w2+w3+…..+w25 = TwB (written shortly);

\Rightarrow \frac{TwB}{25}=42

\Rightarrow TwB=42\times 25

\Rightarrow TwB=1050



Similarly, supposing there are ‘y’ girls, then  for girls we can write;

\Rightarrow \frac{TwG}{y}=33

\Rightarrow TwG=33y

But we are given that average weight of all girls and boys is 38;

\Rightarrow \frac{Weight Of All Girls+Boys}{Number of All Girls+Boys}=38

\Rightarrow \frac{TwB+TwG}{25+y}=38

\Rightarrow \frac{1050+33y}{25+y}=38

\Rightarrow 1050+33y=38(25+y)

\Rightarrow 1050+33y=950+38y

\Rightarrow 1050-950=38y-33y

\Rightarrow 100=5y

\Rightarrow 20=y

So, there are 20 boys.

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