Chapter 12.7, Problem 51E

To determine

To find the number of each type of questions that should be answered to receive the highest score.

Answer to Problem 51E

The number of MCQ questions answered should be $24$ and the number of essay questions answered should be $6$

Explanation of Solution

Given:

Total questions to be answered $=30$ . There are two types of question one is MCQ and other is essay type questions. Total time allotted is two $48$ minute class periods. The MCQ question takes $1$ minute, earns $5$ points and $12$ minutes for each essay question earns $20$ points.

Calculation:

Let the number of MCQ questions answered be $x$

And the number of essay questions answered be $30-x$

Now, according to question-

  $\begin{array}{l}x(1)+(30-x)(12)=2\times 48\\ x+360-12x=96\\ 264=11x\\ x=24\end{array}$

Therefore, the number of MCQ questions answered should be $24$ and the number of essay questions answered should be $30-24=6$

The maximum score in given time period is $24\times 5+6\times 20=120+120=240$