Question:
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 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
Show Hint
Let each paper carry F marks. Use the 60% overall condition to find the actual marks in each paper as a percentage of F.
Updated On: Nov 4, 2026
- 2
- 4
- 3
- 5
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Set up the marks:
Let the full marks of each paper be \(F\). The total full marks are \(5F\). The marks in the five papers are \(6k,\,7k,\,8k,\,9k,\,10k\), so the total marks obtained are \(40k\).
Step 2: Use the 60% condition:
\(40k = 0.60 \times 5F = 3F\), so \(k = \dfrac{3F}{40}\).
Step 3: Find the percentage in each paper:
Paper 1: \(6k = \dfrac{18F}{40} = 45\%\) of \(F\).
Paper 2: \(7k = \dfrac{21F}{40} = 52.5\%\).
Paper 3: \(8k = \dfrac{24F}{40} = 60\%\).
Paper 4: \(9k = \dfrac{27F}{40} = 67.5\%\).
Paper 5: \(10k = \dfrac{30F}{40} = 75\%\).
Step 4: Count:
Only the first paper (45%) is not above 50%. The other four papers are above 50%.
Final Answer:
The correct option is (2): 4
Let the full marks of each paper be \(F\). The total full marks are \(5F\). The marks in the five papers are \(6k,\,7k,\,8k,\,9k,\,10k\), so the total marks obtained are \(40k\).
Step 2: Use the 60% condition:
\(40k = 0.60 \times 5F = 3F\), so \(k = \dfrac{3F}{40}\).
Step 3: Find the percentage in each paper:
Paper 1: \(6k = \dfrac{18F}{40} = 45\%\) of \(F\).
Paper 2: \(7k = \dfrac{21F}{40} = 52.5\%\).
Paper 3: \(8k = \dfrac{24F}{40} = 60\%\).
Paper 4: \(9k = \dfrac{27F}{40} = 67.5\%\).
Paper 5: \(10k = \dfrac{30F}{40} = 75\%\).
Step 4: Count:
Only the first paper (45%) is not above 50%. The other four papers are above 50%.
Final Answer:
The correct option is (2): 4
Was this answer helpful?
0
0
Top CAT Quantitative Aptitude Questions
- In a triangle ABC,AB=AC=8cm. A circle drawn with BC as diameter passes through A. Another circle drawn with center at A passes through B and C. Then the area,in sq.cm,of the overlapping region between the two circles is
- The simple interest accrued on an amount of Rs.25,000 at the end of three years is Rs.7,500. What would be the compound interest accrued on the same amount at the same rate in the same period?
- What is the sum of all roots of the equation \(|x+4|^2–10|x+4|=24\)?
- A solid metal sphere is melted and smaller spheres of equal radii are formed. 10% of the volume of the sphere is lost in the process. The smaller spheres have a radius which is \(\frac{1}{9}\text{th}\) the larger sphere. If 10 litres of paint were needed to paint the larger sphere,how many litres are needed to paint all the smaller spheres?
- The ratio of the ages of a husband and his wife when they got married was 6:5. 4 years and 6 years after their marriage they had their 1st and 2nd children. The sum of the present ages of the husband and wife is 6.4 times the sum of the present ages of their children. The average age of the family at present is 18.5 years. Find the ratio of the ages of the husband and wife when their second child was born.
View More Questions
Top CAT Ratio Questions
- The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157:3, then the sum of the two numbers is
- If the rectangular faces of a brick have their diagonals in the ratio 3: 2√3 :√15, then the ratio of the length of the shortest edge of the brick to that of its longest edge is
- In an examination, Rama's score was one-twelfth of the sum of the scores of Mohan and Anjali. After a review, the score of each of them increased by 6. The revised scores of Anjali, Mohan, and Rama were in the ratio 11:10:3. Then Anjali's score exceeded Rama's score by
- Out of 40 members of team A only 60% are selected for the tour and out of 60 members of team B only 40% are selected for the tour. Ratio of male members to female members on the tour is 5:3. Ratio of male members who are selected from team A to female members who are selected from team A is 5:1. Find total number of female members who are selected for tour from team B.
- Raju and Lalitha originally had marbles in the ratio 4:9. Then Lalitha gave some of her marbles to Raju. As a result, the ratio of the number of marbles with Raju to that with Lalitha became 5:6. What fraction of her original number of marbles was given by Lalitha to Raju?
View More Questions
Top CAT Questions
- Compare and contrast between Portia and Jessica characters in Merchant of Venice.
- In a triangle ABC,AB=AC=8cm. A circle drawn with BC as diameter passes through A. Another circle drawn with center at A passes through B and C. Then the area,in sq.cm,of the overlapping region between the two circles is
- The simple interest accrued on an amount of Rs.25,000 at the end of three years is Rs.7,500. What would be the compound interest accrued on the same amount at the same rate in the same period?
- What is the sum of all roots of the equation \(|x+4|^2–10|x+4|=24\)?
- A solid metal sphere is melted and smaller spheres of equal radii are formed. 10% of the volume of the sphere is lost in the process. The smaller spheres have a radius which is \(\frac{1}{9}\text{th}\) the larger sphere. If 10 litres of paint were needed to paint the larger sphere,how many litres are needed to paint all the smaller spheres?
View More Questions