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Application of Negative Numbers in Everyday Life

Anna ranked 1...

Question

Anna ranked 12th from the top and 31st from the bottom among those who passed an examination. If 8 students did not participate in the exam and 7 students failed it, how many total students are there in the grade?

(The students who failed the exam do not appear on the rank list.)

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Solution

Anna ranked 12th from the top in the examination.

$⟹ N u m b e r o f s t u d e n t s w h o r a n k e d a b o v e A n n a = 12 - 1 = 11$

Anna also ranked 31st from the bottom.

$⟹ N u m b e r o f s t u d e n t s w h o r a n k e d b e l o w A n n a = 31 - 1 = 30$

So, the total number of students who appeared on the rank list will be all the students who ranked above and below Anna including her.

$⟹ T o t a l n u m b e r o f s t u d e n t s w h o a p p e a r e d i n t h e r a n k l i s t = 11 + 30 + 1 = 42$

Now, the students who did not appear in the rank list include those who did not appear for the examination as well as those who failed it.

$⟹ N u m b e r o f s t u d e n t s w h o d i d n o t a p p e a r o n t h e r a n k l i s t = 8 + 7 = 15$

Now, the total number of students in the grade will include the students who appeared on the rank list as well as those who did not.

$⟹ T o t a l n u m b e r o f s t u d e n t s i n g r a d e = 42 + 15 = 57$

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