Question 53

In a class with a certain number of students, if one student weighing 50 kg is added then the average weight of the class increases by 1 kg. If one more student weighing 50 kg is added then the average weight of the class increases by 1.5 kg over the original average. What is the original average weight (in kg) of the class?

Solution

Let number of students in class be $$x$$ and average weight of class be $$y$$ kg

=> Total weight of class = $$xy$$ kg

According to ques, => $$\frac{xy+50}{x+1}=y+1$$

=> $$xy+50=xy+x+y+1$$

=> $$x+y=49$$ ------------(ii)

Similarly, $$\frac{xy+100}{x+2}=y+1.5$$

=> $$xy+100=xy+1.5x+2y+3$$

=> $$1.5x+2y=97$$ ------------(ii)

Solving equations (i) and (ii), we get : $$x=2$$ and $$y=47$$

$$\therefore$$ Original average weight = 47 kg

=> Ans - (D)

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