The given graph shows the performance of the students of schools A, B, C, D, E and F in a Board Examination. Study the graph and answer the questions that follow.
The average number of students (per school) who failed in schools A, B C and E is approximately what percentage less than the number of students who passed without distinction in school D?
Solution
School   Total    Passed    Distinction    Without distinction   Failed
AÂ Â Â Â Â Â Â 800Â Â Â Â Â Â Â 640Â Â Â Â Â Â Â 300Â Â Â Â Â Â Â Â Â Â Â Â Â 340Â Â Â Â Â Â Â Â Â Â Â Â 160
BÂ Â Â Â Â Â Â 1050Â Â Â Â Â Â 840Â Â Â Â Â Â Â Â 350Â Â Â Â Â Â Â Â Â Â Â Â 490Â Â Â Â Â Â Â Â Â Â Â 210
CÂ Â Â Â Â Â Â 1200Â Â Â Â Â Â 920Â Â Â Â Â Â Â Â 450Â Â Â Â Â Â Â Â Â Â Â Â 470Â Â Â Â Â Â Â Â Â Â Â 280
DÂ Â Â Â Â Â Â 750Â Â Â Â Â Â Â 600Â Â Â Â Â Â Â Â 260Â Â Â Â Â Â Â Â Â Â Â Â 340Â Â Â Â Â Â Â Â Â Â Â Â 150
EÂ Â Â Â Â Â Â 900Â Â Â Â Â Â 750Â Â Â Â Â Â Â Â 330Â Â Â Â Â Â Â Â Â Â Â Â Â 420Â Â Â Â Â Â Â Â Â Â Â 150
FÂ Â Â Â Â Â Â 1500Â Â Â Â Â Â 1000Â Â Â Â Â Â Â 450Â Â Â Â Â Â Â Â Â Â Â Â Â 550Â Â Â Â Â Â Â Â Â Â Â 500
Using our collected data, we can easily calculate the average number of students who failed in A, B, C and E to be $$(160+210+280+150)/4=800/4=200$$
The number of students who passed without distinction is 340.
Ratio of these two values is $$\frac{200}{340}=0.588$$
Which means that the average number of students who failed in A, B, C and E is 41.176% smaller than the number of students who passed without distinction in D.Â
This is approximately 41%.Â
Therefore, Option A is the correct answer.Â
