FOR EXAMPLE:

(Q1) A candidate who scores 30% fails by 5 marks, while another candidate who scores 40% marks get 10 more then minimum pass marks. The minimum marks required to pass are.

Solution:Let total marks=100x

Now,

100x×(30/100)+5=100x×(40/100)-10

=>30x+5=40x-10

=>30x-40x=-10-5

=.-10x=-15

∴x=15/10

Total marks=100x

=100×(15/10)

=150

∴ minimum marks=100x×(30/100)+5

=100×(15/10)×(30/100)+5

=50 Ans

Concepts:[According to question A candidate who scores 30% fails by 5 marks.that means इस candidate को minimum pass marks  के लिए 5 marks अधिक लना चाहिए था  i.e 100x×(30/100)+5 marks लाना चाहिए था|

now another candidate who scores 40% marks get 10 more than minimum passing marks.that means इस candidate को minimum pass marks के लिए 10 marks कम लाना चाहिए था i.e 100x×(40/100)-10 लाना चाहिए था|]

(Q2)In an examination, a candidate must secure 40% marks to pass. A candidate, who gets 220 marks fails by 20 marks. what are the maximum marks for the examination?

Solution:Let maximum marks=100x

now,

100x×(40/100) =220+20

40x=240

∴ x=6

maximum marks=100x

=100×6

600 Ans.

Concept:[220 marks लाया and  20 marks से fail हो गया that means उसे pass होने के लिये (220+20)marks लाना होगा]

(Q3)In an examination, there are three papers and a candidate has got 35% of the total to pass. in one paper ,he gets 62 out of 150 and in the second 35 out of 150. how much he get, out of 180, In the third paper to just qualify for a pass.

Solution: Let the marks required in the third paper= x.

then,

(62+35+x)=35% of(150+150+180)

=>97+x=(35/100)×480

∴ x=168-97

=71 Ans.

(Q4)In an examination, there are three subjects of 100 marks each. A student scores 60% in the first subject and 80% in the second subject. He scored 70% in aggregate. His percentage of marks in the third subjects is.

Solution: let percentage marks in third subjects=x

then,

60+80+x=70% of (100+100+100)

=>140+x=(70/100)×300

∴ x=70 i.e 70% Ans.

(Q5)In an examination,65% of the students passed in mathematics, 48% passed in physics and 30% passed in both. How much percent of students failed in both the subjects?

Solution:

Students passed only in mathematics=65%-30%=35%

Students passed only in physics=48%-30%=18%

students passed in both subjects=30%

total pass=35%+18%+30%

=83%

∴ total failed in both subjects=100%-83%

=17% Ans.

BY TRICK:

Percentage of students who passed in either mathematics or physics or both=(65+48-30)%=83%

∴ total failed in both subjects=100%-83%

=17% Ans.

(Q6)In an examination, 75% candidate who passed in English and 60% passed in mathematics. 25% failed in both the subjects. If 240 candidate passed in both.Find the total number of candidates.

Solution:Let x candidates passed in both subjects.

percentage of students who passed in either English or mathematics or both=(75+60-x)%

=>75%=(135-x)%

∴ x=60%

Now,

60%=240

∴ 1%=240/60

∴ 100%=(240/60)×100

=400 candidate Ans.

Concept:[25% failed in both subjects it means only 75% candidates passed in either English or mathematics or both]

(Q7)In an examination A got 25% marks more than B, B got 10% less than C and C got 25% more than D. if D got 320 marks out of 500, the marks obtained by A.

Solution:

(Q8)Three sets of 40,50 and 60 students appeared for an examination and the pass percentage was 100,90 and 80 respectively. The pass percentage of the whole set is.

Solution:pass percentage of the whole set=(40×100+90×50+60×80)/(40+50+60)

                                                                                   =88²/3% Ans.