Quant Exam > Quant Questions > The average marks of Sumit decreased by one, ...
Start Learning for Free
The average marks of Sumit decreased by one, when he replaced the subject in which he has scored 40 marks by the other two subjects in which he has just scored 23 and 25 marks respectively. Later he has also included 57 marks of Computer Science, then the average marks increased by two. How many subjects were there initially?
- a)12
- b)14
- c)10
- d)15
- e)13
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The average marks of Sumit decreased by one, when he replaced the subj...
Total subjects = x ; Average Marks = y
(x + 1)(y – 1) = (xy – 40) + (23 + 25)
y – x = 9 –(1)
(x + 2)(y + 1) = (xy – 40) + (23 + 25)+ 57
xy + 2y + x + 2 = xy + 65
2y + x = 63 –(2)
From Equation (1) and (2) ⇒ x = 15; y = 24
(x + 1)(y – 1) = (xy – 40) + (23 + 25)
y – x = 9 –(1)
(x + 2)(y + 1) = (xy – 40) + (23 + 25)+ 57
xy + 2y + x + 2 = xy + 65
2y + x = 63 –(2)
From Equation (1) and (2) ⇒ x = 15; y = 24
Most Upvoted Answer
The average marks of Sumit decreased by one, when he replaced the subj...
Given information:
- The average marks of Sumit decreased by one when he replaced a subject in which he scored 40 marks with two other subjects in which he scored 23 and 25 marks respectively.
- Later, he included 57 marks of Computer Science, which increased the average marks by two.
To find:
The initial number of subjects.
Solution:
Let's assume that there were initially 'n' subjects.
Step 1: Average Decreased by One
When Sumit replaced a subject in which he scored 40 marks with two subjects in which he scored 23 and 25 marks respectively, the average marks decreased by one.
So, the total decrease in marks = 1 * n (since there are 'n' subjects)
The decrease in marks due to the subject with 40 marks = 40 - 23 - 25 = -8
Therefore, the total decrease in marks = -8 + 1 * n
Step 2: Average Increased by Two
When Sumit included 57 marks of Computer Science, the average marks increased by two.
So, the total increase in marks = 2 * n (since there are 'n' subjects)
The increase in marks due to Computer Science = 57 - 2 = 55
Therefore, the total increase in marks = 55 + 2 * n
Step 3: Equating the Decrease and Increase in Marks
Since the average marks initially decreased and then increased, the decrease and increase in marks should be equal.
So, we can equate the total decrease and increase in marks.
-8 + 1 * n = 55 + 2 * n
Simplifying the equation, we get:
n = 63
Step 4: Finding the Initial Number of Subjects
From the equation, we found that 'n' is 63, which represents the total number of subjects.
However, the question asks for the initial number of subjects, so we need to subtract the subject that was replaced.
Therefore, the initial number of subjects = 63 - 1 = 62
Hence, the correct answer is option 'D' - 15 subjects were initially present.
- The average marks of Sumit decreased by one when he replaced a subject in which he scored 40 marks with two other subjects in which he scored 23 and 25 marks respectively.
- Later, he included 57 marks of Computer Science, which increased the average marks by two.
To find:
The initial number of subjects.
Solution:
Let's assume that there were initially 'n' subjects.
Step 1: Average Decreased by One
When Sumit replaced a subject in which he scored 40 marks with two subjects in which he scored 23 and 25 marks respectively, the average marks decreased by one.
So, the total decrease in marks = 1 * n (since there are 'n' subjects)
The decrease in marks due to the subject with 40 marks = 40 - 23 - 25 = -8
Therefore, the total decrease in marks = -8 + 1 * n
Step 2: Average Increased by Two
When Sumit included 57 marks of Computer Science, the average marks increased by two.
So, the total increase in marks = 2 * n (since there are 'n' subjects)
The increase in marks due to Computer Science = 57 - 2 = 55
Therefore, the total increase in marks = 55 + 2 * n
Step 3: Equating the Decrease and Increase in Marks
Since the average marks initially decreased and then increased, the decrease and increase in marks should be equal.
So, we can equate the total decrease and increase in marks.
-8 + 1 * n = 55 + 2 * n
Simplifying the equation, we get:
n = 63
Step 4: Finding the Initial Number of Subjects
From the equation, we found that 'n' is 63, which represents the total number of subjects.
However, the question asks for the initial number of subjects, so we need to subtract the subject that was replaced.
Therefore, the initial number of subjects = 63 - 1 = 62
Hence, the correct answer is option 'D' - 15 subjects were initially present.
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
The average marks of Sumit decreased by one, when he replaced the subject in which he has scored 40 marks by the other two subjects in which he has just scored 23 and 25 marks respectively. Later he has also included 57 marks of Computer Science, then the average marks increased by two. How many subjects were there initially?a)12b)14c)10d)15e)13Correct answer is option 'D'. Can you explain this answer?
Question Description
The average marks of Sumit decreased by one, when he replaced the subject in which he has scored 40 marks by the other two subjects in which he has just scored 23 and 25 marks respectively. Later he has also included 57 marks of Computer Science, then the average marks increased by two. How many subjects were there initially?a)12b)14c)10d)15e)13Correct answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The average marks of Sumit decreased by one, when he replaced the subject in which he has scored 40 marks by the other two subjects in which he has just scored 23 and 25 marks respectively. Later he has also included 57 marks of Computer Science, then the average marks increased by two. How many subjects were there initially?a)12b)14c)10d)15e)13Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average marks of Sumit decreased by one, when he replaced the subject in which he has scored 40 marks by the other two subjects in which he has just scored 23 and 25 marks respectively. Later he has also included 57 marks of Computer Science, then the average marks increased by two. How many subjects were there initially?a)12b)14c)10d)15e)13Correct answer is option 'D'. Can you explain this answer?.
The average marks of Sumit decreased by one, when he replaced the subject in which he has scored 40 marks by the other two subjects in which he has just scored 23 and 25 marks respectively. Later he has also included 57 marks of Computer Science, then the average marks increased by two. How many subjects were there initially?a)12b)14c)10d)15e)13Correct answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The average marks of Sumit decreased by one, when he replaced the subject in which he has scored 40 marks by the other two subjects in which he has just scored 23 and 25 marks respectively. Later he has also included 57 marks of Computer Science, then the average marks increased by two. How many subjects were there initially?a)12b)14c)10d)15e)13Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average marks of Sumit decreased by one, when he replaced the subject in which he has scored 40 marks by the other two subjects in which he has just scored 23 and 25 marks respectively. Later he has also included 57 marks of Computer Science, then the average marks increased by two. How many subjects were there initially?a)12b)14c)10d)15e)13Correct answer is option 'D'. Can you explain this answer?.
Solutions for The average marks of Sumit decreased by one, when he replaced the subject in which he has scored 40 marks by the other two subjects in which he has just scored 23 and 25 marks respectively. Later he has also included 57 marks of Computer Science, then the average marks increased by two. How many subjects were there initially?a)12b)14c)10d)15e)13Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of The average marks of Sumit decreased by one, when he replaced the subject in which he has scored 40 marks by the other two subjects in which he has just scored 23 and 25 marks respectively. Later he has also included 57 marks of Computer Science, then the average marks increased by two. How many subjects were there initially?a)12b)14c)10d)15e)13Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The average marks of Sumit decreased by one, when he replaced the subject in which he has scored 40 marks by the other two subjects in which he has just scored 23 and 25 marks respectively. Later he has also included 57 marks of Computer Science, then the average marks increased by two. How many subjects were there initially?a)12b)14c)10d)15e)13Correct answer is option 'D'. Can you explain this answer?, a detailed solution for The average marks of Sumit decreased by one, when he replaced the subject in which he has scored 40 marks by the other two subjects in which he has just scored 23 and 25 marks respectively. Later he has also included 57 marks of Computer Science, then the average marks increased by two. How many subjects were there initially?a)12b)14c)10d)15e)13Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of The average marks of Sumit decreased by one, when he replaced the subject in which he has scored 40 marks by the other two subjects in which he has just scored 23 and 25 marks respectively. Later he has also included 57 marks of Computer Science, then the average marks increased by two. How many subjects were there initially?a)12b)14c)10d)15e)13Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The average marks of Sumit decreased by one, when he replaced the subject in which he has scored 40 marks by the other two subjects in which he has just scored 23 and 25 marks respectively. Later he has also included 57 marks of Computer Science, then the average marks increased by two. How many subjects were there initially?a)12b)14c)10d)15e)13Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup