d Word Problems 7 & 8 | Job Exam Rare Mathematics (JEMrare) - Solved MCQs

Word Problems 7 & 8

Problem 7: There are 40 boys in a class. One of them weighing 100 lbs goes away, a new boy joins the class at the same time. The average weight of the boys is thus increased by 1/4 lbs, Find the weight of the new boy.


Suppose there are 39 boys in class whose weight is x1,x2,x3 ………x39 and one boy (40th) has wieght of 100lb.

So their average weight is ‘y’ then;

\Rightarrow y=\frac{x1+x2+x3+...........+x39+100lb}{40}

\Rightarrow x1+x2+x3+...........+x39=40y-100-----(1)

Now suppose 100lb boy leaves away and new boy comes whose weight is ‘zlb’

Then again average weight of 40 including new boys is calculated as;

\Rightarrow Average Age Of 40 Students including New Boy= \frac{x1+x2+x3+...........+x39+z}{40}

Put values of x1+x2+x3+……..+x39 from eq (1) above, we get;

\Rightarrow Average Age Of 40 Students including New Boy= \frac{40y-100+z}{40}

But ,

Average Age Of 40 Students including New Boy= y+\frac{1}{4}


\Rightarrow y+\frac{1}{4}= \frac{40y-100+z}{40}

\Rightarrow \frac{4y+1}{4}= \frac{40y-100+z}{40}

\Rightarrow 10(4y+1)= 40y-100+z

\Rightarrow 40y+10= 40y-100+z

\Rightarrow 10= -100+z

\Rightarrow 10+100= +z

\Rightarrow 10+100= z

\Rightarrow 110= z


\Rightarrow z=110

So, the weight of new boy is 110 lb

Problem 8: The average age of a class of 20 boys is 14.95 years. The avaerage age of the class is raised to 15 years by the arrival of a new student. How old is that new boy?


Let’s suppose  ages of 20 students be x1,x2,x3………………..x20

Then average age of 20 students is obtained by taking sum of their ages and dividing the sum by number of student i-e20;

\Rightarrow Average Age Of 20 Students= \frac{x1+x2+x3+...........+x20}{20}

But average of 20 students is given to be 14.96 in statement;

\Rightarrow 14.96= \frac{x1+x2+x3+...........+x20}{20}

\Rightarrow 14.96 \times 20= x1+x2+x3+...........+x20

\Rightarrow x1+x2+x3+...........+x20=299 ----(1)

Let new boy’s age is ‘y’ years

Now average age of total 21 boys is given by;

\Rightarrow Average Age Of 21 Students= \frac{x1+x2+x3+...........+x20+y}{21}

But average age of 21 students is given to be 15 years

\Rightarrow 15= \frac{x1+x2+x3+...........+x20+y}{21}

Put value of x1+x2+x3+…….+x20   here;

\Rightarrow 15= \frac{299+y}{21}

\Rightarrow 15\times 21 =299+y

\Rightarrow 315 =299+y

\Rightarrow y=315-299

\Rightarrow y=16

So, the age of new boy is 16 years



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