d Problem 5: The average weight of 5 men is increased by 1 kg, when one of them whose weight is 60 kgs, is replaced by a new man. What is the weight of the new man? | Job Exam Rare Mathematics (JEMrare) - Solved MCQs
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Problem 5: The average weight of 5 men is increased by 1 kg, when one of them whose weight is 60 kgs, is replaced by a new man. What is the weight of the new man?

Problem 5: The average weight of 5 men is increased by 1 kg, when one of them whose weight is 60 kgs, is replaced by a new man. What is the weight of the new man?

a) 64 kgs                  b) 65 kgs                   c) 50 kgs                  55 kgs

Solution:

Let there be 5 men whose weights are m1, m2, m3, m4 and 60. Let their average weight be ‘x’;

\Rightarrow x = \frac{m1+m2+m3+m4+60}{5}

\Rightarrow m1+m2+m3+m4+60=5x

\Rightarrow m1+m2+m3+m4=5x-60 ----(1)

Now let the man weighing 60 kg is replaced by a man whose weight is ‘M’. As per condition average weight now becomes x+1;

\Rightarrow x+1=\frac{m1+m2+m3+m4+M}{5}

\Rightarrow m1+m2+m3+m4+M=5(x+1)

\Rightarrow m1+m2+m3+m4=5(x+1)-M

Put value of m1+m2+m3+m4 from eq(1);

\Rightarrow 5x-60=5(x+1)-M

\Rightarrow 5x-60=5x+5-M

\Rightarrow -60=5-M

\Rightarrow -60-5=-M

\Rightarrow -65=-M

\Rightarrow M=65

So, the weight of new man is 65 kg



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