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A certain number of chocolates are equally distributed among a certain number of students in such a way that each student gets 14 chocolates. However, if 4 of those students decide to distribute their chocolates equally amongst themselves, then the students who have not distributed their share get 4 extra chocolates. Find the total number of chocolates.
Correct answer is '196'. Can you explain this answer?
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Verified Answer
A certain number of chocolates are equally distributed among a certain...
Let the total number of students be x.
The total number of chocolates = 14x
The total number of chocolates = 14x
Four students amongst them will now distribute 4 x 14 = 56 chocolates
This is equal to the number of chocolates which are recieved by all of them in this distribution = 4x
4x = 56 i.e. x = 14 Thus, there are 14 x 14 = 196 chocolates.
Answer: 196
Most Upvoted Answer
A certain number of chocolates are equally distributed among a certain...
Given information:
- Each student initially gets 14 chocolates
- Some students decide to distribute their chocolates equally among themselves
- After redistribution, the remaining students get 4 extra chocolates each
To find: Total number of chocolates
Let there be 'x' number of students initially.
Initial Distribution:
- Each student gets 14 chocolates
- So, the total number of chocolates distributed = 14x
Redistribution:
- Let there be 'y' students who decided to redistribute their chocolates
- So, the number of chocolates each of these students had initially = 14
- After redistribution, each of them will have x chocolates each
- So, the total number of chocolates redistributed = y * (x-14)
Remaining Students:
- After redistribution, 'x-y' students did not participate
- Each of these students gets 4 extra chocolates
- So, the total number of extra chocolates distributed = 4 * (x-y)
Total Number of Chocolates:
- The total number of chocolates distributed = the total number of chocolates redistributed + the total number of extra chocolates distributed
- Therefore, 14x = y * (x-14) + 4 * (x-y)
Simplifying the equation:
- 14x = xy - 14y + 4x - 4y
- 10x = xy - 10y
- 10x = y(x-10)
Since the number of chocolates redistributed cannot be greater than the number of chocolates initially distributed, we must have:
- y <= x/14="">
Also, y cannot be 0, as the question states that some students decided to redistribute their chocolates.
- So, y >= 1
Using these constraints, we can find the possible values of x and y that satisfy the equation.
One possible solution is:
- x = 28
- y = 20
Substituting these values in the equation:
- 14x = y * (x-14) + 4 * (x-y)
- 14*28 = 20 * (28-14) + 4 * (28-20)
- 392 = 400
This is not possible, as the equation does not hold true.
Trying another solution:
- x = 56
- y = 40
Substituting these values in the equation:
- 14x = y * (x-14) + 4 * (x-y)
- 14*56 = 40 * (56-14) + 4 * (56-40)
- 784 = 784
This solution satisfies the equation, so the total number of chocolates is:
- 14x = 14*56 = 784
Therefore, the total number of chocolates is 784.
- Each student initially gets 14 chocolates
- Some students decide to distribute their chocolates equally among themselves
- After redistribution, the remaining students get 4 extra chocolates each
To find: Total number of chocolates
Let there be 'x' number of students initially.
Initial Distribution:
- Each student gets 14 chocolates
- So, the total number of chocolates distributed = 14x
Redistribution:
- Let there be 'y' students who decided to redistribute their chocolates
- So, the number of chocolates each of these students had initially = 14
- After redistribution, each of them will have x chocolates each
- So, the total number of chocolates redistributed = y * (x-14)
Remaining Students:
- After redistribution, 'x-y' students did not participate
- Each of these students gets 4 extra chocolates
- So, the total number of extra chocolates distributed = 4 * (x-y)
Total Number of Chocolates:
- The total number of chocolates distributed = the total number of chocolates redistributed + the total number of extra chocolates distributed
- Therefore, 14x = y * (x-14) + 4 * (x-y)
Simplifying the equation:
- 14x = xy - 14y + 4x - 4y
- 10x = xy - 10y
- 10x = y(x-10)
Since the number of chocolates redistributed cannot be greater than the number of chocolates initially distributed, we must have:
- y <= x/14="">
Also, y cannot be 0, as the question states that some students decided to redistribute their chocolates.
- So, y >= 1
Using these constraints, we can find the possible values of x and y that satisfy the equation.
One possible solution is:
- x = 28
- y = 20
Substituting these values in the equation:
- 14x = y * (x-14) + 4 * (x-y)
- 14*28 = 20 * (28-14) + 4 * (28-20)
- 392 = 400
This is not possible, as the equation does not hold true.
Trying another solution:
- x = 56
- y = 40
Substituting these values in the equation:
- 14x = y * (x-14) + 4 * (x-y)
- 14*56 = 40 * (56-14) + 4 * (56-40)
- 784 = 784
This solution satisfies the equation, so the total number of chocolates is:
- 14x = 14*56 = 784
Therefore, the total number of chocolates is 784.
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Community Answer
A certain number of chocolates are equally distributed among a certain...
I think the answer should be 252. since originally 18 students are there. 4 of them decided to give away their chocolate. so now 14 students get 18 chocolate. hence, each gets 4 extra.
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A certain number of chocolates are equally distributed among a certain number of students in such a way that each student gets 14 chocolates. However, if 4 of those students decide to distribute their chocolates equally amongst themselves, then the students who have not distributed their share get 4 extra chocolates. Find the total number of chocolates.Correct answer is '196'. Can you explain this answer?
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A certain number of chocolates are equally distributed among a certain number of students in such a way that each student gets 14 chocolates. However, if 4 of those students decide to distribute their chocolates equally amongst themselves, then the students who have not distributed their share get 4 extra chocolates. Find the total number of chocolates.Correct answer is '196'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A certain number of chocolates are equally distributed among a certain number of students in such a way that each student gets 14 chocolates. However, if 4 of those students decide to distribute their chocolates equally amongst themselves, then the students who have not distributed their share get 4 extra chocolates. Find the total number of chocolates.Correct answer is '196'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain number of chocolates are equally distributed among a certain number of students in such a way that each student gets 14 chocolates. However, if 4 of those students decide to distribute their chocolates equally amongst themselves, then the students who have not distributed their share get 4 extra chocolates. Find the total number of chocolates.Correct answer is '196'. Can you explain this answer?.
A certain number of chocolates are equally distributed among a certain number of students in such a way that each student gets 14 chocolates. However, if 4 of those students decide to distribute their chocolates equally amongst themselves, then the students who have not distributed their share get 4 extra chocolates. Find the total number of chocolates.Correct answer is '196'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A certain number of chocolates are equally distributed among a certain number of students in such a way that each student gets 14 chocolates. However, if 4 of those students decide to distribute their chocolates equally amongst themselves, then the students who have not distributed their share get 4 extra chocolates. Find the total number of chocolates.Correct answer is '196'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain number of chocolates are equally distributed among a certain number of students in such a way that each student gets 14 chocolates. However, if 4 of those students decide to distribute their chocolates equally amongst themselves, then the students who have not distributed their share get 4 extra chocolates. Find the total number of chocolates.Correct answer is '196'. Can you explain this answer?.
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