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A student took five papers in an examination, where the full marks

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A student took five papers in an examination, where the full marks [#permalink]

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A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is

a. 2
b. 3
c. 4
d. 5
e. 1

Source- quant4gmat
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A student took five papers in an examination, where the full marks [#permalink]

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Here we can assume that one subject is of 100 marks so total there are 5 subjects => 100*5 = 500.
Now according to the question he secured 60 % of those which is 60%of 500 = 300 marks in total.

The ratio between the marks is given as 6 : 7 : 8 : 9 : 10 , so now we can distribute 300 marks according to the ratio.

Total ratio = 40
For 6 : (300/40)*6 = 45
Similarly , we will get for others as 52.5 , 60 , 62.5 , 75.

Hence , there are 4 subject where he secured more that 50 %.

The answer is 4.

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Re: A student took five papers in an examination, where the full marks [#permalink]

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New post 22 Dec 2017, 12:44
Total ratio = 40
How?
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Re: A student took five papers in an examination, where the full marks [#permalink]

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New post 22 Dec 2017, 13:15
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By saying total ratio = 40, he is adding the ratio values 6,7,8,9,10.
we can assume 6x,7x,8x,9x,10x.

So 6x+7x+8x+9x+10x = 300
x = 300/40 = 7.5

We can exam marks as 42.5(6x), 52.5(7x)...

so 4 subjects having >50%.
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Re: A student took five papers in an examination, where the full marks [#permalink]

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New post 22 Dec 2017, 18:45
I don't get the part " more than 50% marks"
50% of what? because these are just MARKS "Similarly , we will get for others as 52.5 , 60 , 62.5 , 75." not % marks.
Can anyone explain for me please?
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Re: A student took five papers in an examination, where the full marks [#permalink]

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New post 22 Dec 2017, 19:13
A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is ...

Lets assume each paper of 100 marks, overall obtained marks = 5*100*0.6 = 300

After that you can refer to previous post for solution...
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Re: A student took five papers in an examination, where the full marks [#permalink]

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New post 22 Dec 2017, 23:17
excelingmat wrote:
A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is

a. 2
b. 3
c. 4
d. 5
e. 1

Source- quant4gmat

Let's consider 'x' as common multiplier. Then summation of scores in all 5 papers will be 6x+7x+8x+9x+10x=40x
Now this summation is 60% total marks. Let's consider 400 as total marks(400 is divisible by 40 an 100 both).
So student obtained total of 240 marks. If we divide 240 by 40x we get value of x=6. Multiply 6 to each ration value of subject and we get marks in each paper as: 36,42,48,54,60. Now maximum total marks that can be obtained is 400 then each paper is of 80 marks. Except 1st paper all 4 papers have > 50% marks
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A student took five papers in an examination, where the full marks [#permalink]

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New post 23 Dec 2017, 05:25
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lichting wrote:
I don't get the part " more than 50% marks"
50% of what? because these are just MARKS "Similarly , we will get for others as 52.5 , 60 , 62.5 , 75." not % marks.
Can anyone explain for me please?


Hi lichting

you can work with simple numbers here. as scores are in the ratio \(6:7:8:9:10\) and \(6+7+8+9+10=40\)

so let's assume total marks in each paper is \(40\). to score more than \(50\)% marks in any paper score has to be \(>20\)

Now we need to find out the papers where he scored\(>20\)

Total possible Marks in all the 5 papers \(= 5*40=200\)

Total marks scored in all 5 paper \(= 60\)% of \(200=120\)

Marks scored in 1st Paper \(= \frac{6}{40}*120=18<20\)

Marks scored in second paper \(= \frac{7}{40}*120=21>20\)

Now we can stop here because ratio of marks scored in other papers are more than 7 (8, 9 & 10), hence scored marks will be more than 20 i.e more than 50%.

So we have 4 papers where he scored more than 50% marks.
A student took five papers in an examination, where the full marks   [#permalink] 23 Dec 2017, 05:25
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