Question 1016103
i think this is what you want to find out.


let x = the maximum score possible.
let y = the passing score.


your first equation is .25x = y - 30


this means a score of 25% of the maximum marks possible is 30 marks below the passing score.


your second equatoon is .50x = y + 20


this means a score of 50% of the maximum marks possible is 20 points above the passing score.


your two equations are:


.25x = y - 30
.50x = y + 20


these are two equations that need to be solved simultaneously.


there are various ways to do that.


i'll do the following:


solve each equation for y to get:


y = .25x + 30
y = .50x - 20


since y = .25x + 30 from the first equation, replace y with .25x + 30 in the second equation to get:


.25x + 30 = .50x - 20


subtract .25x from both sides of this equation and add 20 to both sides of this equation to get:


50 = .25x


divide both sides of this equation by .25 to get:


200 = x


that's the maximum marks that can be attained on the test.


go back to either one of your original equations and replace x with 200 and solve for y.


your original equation for this part of the analysis are after you solved them for y.


they are:


y = .25x + 30
y = .50x - 20


replace x with 200 and these equations become:


y = .25*200 + 30 = 50 + 30 = 80
y = .50*200 - 20 = 100 - 20 = 80


you get y = 80


that's the score required to pass.


the maximum score possible is 200.
the passing score is 80.


to verify that you didn't mess anything up in between, go back to the original problem and see if it makes sense with these numbers.


the original problem states:


A candidate scores 25 percent marks in an examination an failed by 30 marks, while another candidate who scored 50 percent marks got 20 marks more than the minimum pass marks. Find the maximum marks and minimum pass marks. (Give answer with detailed method)


25 percent marks means 25% of the total possible marks.
this is 25 percent of 200 which is equal to 50.
he failed by 30 marks which means the passing marks is 80.


50 percent marks means 50% of the total possible marks.
this is 50 percent of 200 which is equal to 100.
he passed by 20 marks which means the passing mark is 80.


solution checks out.


solution is maximum marks is 200 and minimum passing marks is 80.