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

Solution:

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}

So,

\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

Or

\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?

Solution:

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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