Question

To receive grade 'A' in a course, one must obtain an average of 90 marks or more in five papers each of 100 marks. If Shikha scored 87, 95, 92 and 94 marks in first four paper, find the minimum marks that she must score in the last paper to get grade 'A' in the course.

Answer 1

Let x be the minimum marks scored in the last paper.


$$\begin{gathered} \mathrm{Then,}90\le \frac{87+95+92+94+x}{5}\le 100 \\ \Rightarrow 90\le \frac{368+x}{5}\le 100 \\ \Rightarrow 450\le 368+x\le 500 \\ \Rightarrow 450-368\le 368+x-368\le 500-368 \\ \Rightarrow 82\le x\le 132 \\ \mathrm{But}x\mathrm{can}\mathrm{not}\mathrm{be}\mathrm{more}\mathrm{than}100 \\ \Rightarrow 82\le x\le 100 \\ \mathrm{Hence},\mathrm{the}\mathrm{minimum}\mathrm{marks}\mathrm{that}\mathrm{Shikha}\mathrm{must}\mathrm{score}\mathrm{in}\mathrm{the}\mathrm{fifth}\mathrm{paper}\mathrm{is}82. \end{gathered}$$