So Close To Failing

Let each paper be for 'a' marks...
hence total marks is 5a
ie ... 6x+7x+8x+9x+10x = 3/5 * (5a) (because he obtained 3/5 of the total marks)
therefore 40x = 3a hence x=3a/40
.His total number in 1st paper is = (6*3)a/40 = 0.45(a) ie 45% of a
similarly in 2nd, 3rd, 4th and 5th papers his marks are
52.5% of a , 60% of a, 67.5% of a and 75% of a , respectively .
Clearly he got more than 50% marks in 2nd, 3rd, 4th and 5th papers .
ie he got moer than 50% marks in 4 papers ..... :-)

the proportion of the scores is 6:7:8:9:10 if we add up the proportion we get 40 therefore 40a=3/5 and 1/2=(33.33....)a

(33.333....a)/5 =6.66... there are 4 numbers which are larger than 6.66

6+7+8+9+10=40

40 is three fifths of 66 2/3

Since there are five different tests, each test is out of 13 1/3

Only 6 is less that half of 13 1/3

Let each paper is of y marks so total marks will be of 5y 6:7:8:9:10 is the Proportion. So marks obtained by student in all the 5 papers is equal to =6x+7x+8x+9x+10x =40x Since marks obtained by student in all papers is also 3/5 of 5y Hence 40x=3/5(5y) or x=3y/40 or x=0.075y So mark in paper one =6x=6(0.075y)=0.45y=45% Mark in second paper =7x =0.525y = 52.5% MARK in third paper =8x = 0.6y =60% mark in fourth paper =9x =0.675y=67.5% Mark in fifth paper = 10x =0.75y=75%

Answer: student obtained marks more than 50% in 4 paper.

Let a, b,c,d, e be the total marks the student scored for each paper.

Let k be the common factor for the marks a,b,c,d,e.

a/k:b/k:c/k:d/k:e/k=6:7:8:9:10

Since a,b,c,d,e share a common factor, we can chunk out the single long ratio of five values, to 4 ratios of two values as follow:

a:b=6:7 => 7a=6b,
b:c=7:8 => 8b=7c,
... 9c=8d,
... 10d=9e

Now express a,b,c,d in terms of e: d=0.9e,
c=0.8e,
b=0.7e,
a=0.6e

Let the total maximum marks for each paper that can be scored be T. Since he obtained 3/5 of the total marks of all the papers:

a+b+c+d+e=3/5 (5T),
4e=3T,
e=0.75T

Hence: d=0.9e=0.675T,
c=0.8e=0.6T,
b=0.7e=0.525T,
a=0.6e=0.45T

Since the passing ratio is 0.5T (=50%), the student passed 4 papers out of the 5.

Let total marks be 400. Hence score for each paper 400/5 =80. Student has scored (3/5 * 400) 240 marks. His mark in first paper is 6/40 * 240 = 36, which is less than 50% in a paper (50% of 80 = 40). 2nd paper he scores 7/40 * 240=42, which is greater than 40. As we can clearly see that the numerator in the proceeding ratios is only increasing that is 8/40,9/40 and 10/40, all of the 3 scores will naturally be greater than 42(score in second paper which is greater than 50% of the marks in a given exam). Hence answer is 4 papers where he will score more than 50%.

Let A:B:C:D:E= 6:7:8:9:10 Then let the marks in A=k then in B=7k/6 , C=4k/3, D=3k/2, E=5k/3. Hence total marks in addition of marks of {A+B+C+D+E}={ 40k/6} which is equal to 3x/5, where x=total no. of marks. Now 40k/6 = 3x/5 hence k=9x/100. Now since all paper contain equal no. of total marks hence let total marks in each subject be x' then x=5x' hence k=45x'/100. Now put the value of k in the first equation of marks obtained in A,B,C,D,E and we found that leaving A, student scored more than 50% marks in all other subject.. QED

Let total marks be 400. Hence score for each paper 400/5 =80. Student has scored (3/5 * 400) 240 marks. His mark in first paper is 6/40 * 240 = 36, which is less than 50% in a paper (50% of 80 = 40). 2nd paper he scores 7/40 * 240=42, which is greater than 40. As we can clearly see that the numerator in the proceeding ratios is only increasing that is 8/40,9/40 and 10/40, all of the 3 scores will naturally be greater than 42(score in second paper which is greater than 50% of the marks in a given exam). Hence answer is 4 papers where he will score more than 50%.

let total marks for each paper be x.....then total marks in five paper will be 5x...now 3/5 th of it would be 3x....and now the proportions for each paper are 6/40,7/40,8/40,9/40,10/40......now solving it with 3x we get the the marks in each paper and by diividing it by x and multiplying it by 100 we get the percentage...4 are above 50%