The average marks of Sameer decreased by 1, w | vedclass

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Question

(C) Let the initial number of subjects be $n$ and the initial average marks be $x.$ The total marks initially $= nx.$When one subject with $40$ marks

Vedclass · Accepted Answer

$15$

Vedclass · Answer

(C) Let the initial number of subjects be $n$ and the initial average marks be $x.$ The total marks initially $= nx.$When one subject with $40$ marks is replaced by two subjects with $23$ and $25$ marks,the new number of subjects is $(n+1)$ and the new average is $(x-1).$So,$(n+1)(x-1) = nx - 40 + 23 + 25.$$nx - n + x - 1 = nx + 8 \Rightarrow x - n = 9$ (Equation $I$).Next,when $57$ marks of Computer Science are added,the total number of subjects becomes $(n+2)$ and the average becomes $(x-1) + 2 = x+1.$So,$(n+2)(x+1) = (nx - 40 + 23 + 25) + 57.$$nx + n + 2x + 2 = nx + 65 \Rightarrow n + 2x = 63$ (Equation $II$).From Equation $I$,$x = n + 9.$ Substituting this into Equation $II$:$n + 2(n + 9) = 63 \Rightarrow n + 2n + 18 = 63 \Rightarrow 3n = 45 \Rightarrow n = 15.$Thus,there were $15$ subjects initially.

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