A pupil’s marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half $$\frac{1}{2}$$ . The number of pupils in the class is:
a) 10
b) 20
c) 40
d) 73
Answer: c
Explanation:
$$\eqalign{
& {\text{Let}}\,{\text{there}}\,{\text{be}}\,x\,{\text{pupils}}\,{\text{in}}\,{\text{the}}\,{\text{class}}{\text{.}} \cr
& {\text{Total}}\,{\text{increase}}\,{\text{in}}\,{\text{marks}} = {x \times \frac{1}{2}} = \frac{x}{2} \cr
& \frac{x}{2} = \left( {83 – 63} \right) \cr
& \frac{x}{2} = 20 \cr
& x = 40 \cr} $$
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