"> Word Problem 9 | Job Exam Rare Mathematics (JEMrare)

Word Problem 9

Problem 9: The average age of 600 students in a class is 10.75 years, by enrollment of 40 new students the average age is lowered to 10.437 years. Find the average age of the new students.

a) 6.0                 b) 5.75                     c) 5.15                d) 5.50

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Solution:

Note: We will solve this problem in easy way- though it can be solved in one or two steps in no time !

Suppose there are 600 students with ages,

x1,x2,x3 ………………..x600

Then their average age will be obtained by summing up their ages , divided by number of students i-e 600;

So, \Rightarrow Average Age Of 600 Students= \frac{x1+x2+x3+...........+x600}{600}

But average age of 600 students is given as 10.75

\Rightarrow 10.75 = \frac{x1+x2+x3+...........+x600}{600}

\Rightarrow 10.75 \times 600= x1+x2+x3+...........+x6000

or \Rightarrow x1+x2+x3+...........+x6000=6450 ----(1)

Now suppose new 40 students  have ages y1, y2, y3…………….y40

So now total students are 640.

And average age of 640 students again ca be calculated by summing up their ages and dividing the sum number of students i-e 640

If seen by supposition  , total age of 640 students is

\Rightarrow Avg Age Of 640 Student=\frac{ x1+x2+x3+..........x600+y1+y2+.............y40}{640}

Put value of         x1+x2+x3+……….x600     from eq (1);

\Rightarrow Avg Age Of 640 Student=\frac{ 6450+y1+y2+.............y40}{640}

But it is given that after joining of new 40 student the average age becomes  10.437

\Rightarrow 10.4371=\frac{ 6450+y1+y2+.............y40}{640}

\Rightarrow 10.4371\times 640=6450+y1+y2+.............y40

\Rightarrow 6679.68 =6450+y1+y2+.............y40

\Rightarrow y1+y2+.............y40=6679.68-6450

\Rightarrow y1+y2+.............y40=230

Divide both sides by 40

\Rightarrow \frac{y1+y2+.............y40}{40}=\frac{230}{40}

But,

Average Age Of 40 Students =\frac{y1+y2+.............y40}{40}

\Rightarrow Average Age Of 40 Students= \frac{230}{40}

\Rightarrow Average Age Of 40 Students=5.75 Years