Problem Solving

BTGmoderatorDC 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

Since the ratio 6 : 7 : 8 : 9 : 10 is equally spaced and the full marks are the same for each paper, the average marks in five papers would be the middle-most, i.e., 8. Since it is given that the candidate obtained 60% of the total marks (Average of all the papers), 8 represents 60%.

Needless to state that corresponding percentage marks for 9 would be greater than 60%; same with 10.

Let's check corresponding percentage marks for 7. It is 60%*(7/8) = 52.5% > 50%.
Let's check corresponding percentage marks for 6. It is 60%*(6/8) = 45% < 50%.

So, there are four papers in which he got more than 50% marks.

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorDC 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

Let's let the maximum mark on each paper be 100. So if he earned the maximum mark for each of the five papers, he would have earned 500 marks. However, since he only got 60% of the total marks, he has a total of 0.6 x 500 = 300 marks.

We can let his marks on the five papers be 6n, 7n, 8n, 9n, and 10n, respectively. So we have:

6n + 7n + 8n + 9n + 10n = 300

40n = 300

n = 7.5

Therefore, his marks on the five papers are 45, 52.5, 60, 67.5 and 75. We see that 4 of the 5 papers received a mark higher than 50.

Answer: C