vipinsharma wrote:A student scores 25% and failed by 30 marks while another student who scores 60% gets 40 marks more than minimum required marks to pass. find the maximum marks in the exam.?
When posting questions,
please include the 5 answer choices. In many cases, the fastest approach involves using the answer choices to our advantage.
Here's one approach:
Let T = the TOTAL number of marks the test is out of (i.e., the maximum score)
Let P = the number of marks required to PASS the test
A student scores 25% and failed by 30 marks
In other words, getting 25% of the total possible marks results in a score that's 30 marks LESS THAN the number of marks required to pass.
We can write: 0.25T = P - 30
Rewrite as
0.25T + 30 = P
A student who scores 60% gets 40 marks more than minimum required marks to pass
In other words, getting 60% of the total possible marks results in a score that's 40 marks MORE THAN the number of marks required to pass.
We can write: 0.60T = P + 40
Rewrite as
0.60T - 40 = P
Since the red and blue equations are set equal to
P, we can write...
0.25T + 30 =
0.60T - 40
Rearrange to get: 70 = 0.35T
Solve to get: T =
200
So, the test is out of
200 marks. So, the maximum score is
200.
ASIDE: If the answer choices had been included, it might have been faster to just start testing the answer choices.
ASIDE: If we solve for P, we see that the PASSING score for this test was 80 marks. I mention this because some students might assume that 50% was the passing score for the test.
Cheers,
Brent
