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A man distributed some chocolates among his three children A, B and C (everyone gets at least 4 chocolates). If the man took back one chocolate from C, the total number of chocolates of A and B would be equal to that of C. The number of chocolates of B is the average of number of chocolates of A and C. If B gave 2/3rd of the number of chocolates he had to A, A gave one 2 chocolate to C and then if C gave 2/5th of the number of chocolates he then had to B, then all of them would have equal number of chocolates. How many chocolates did the man distribute?
- a)21
- b)24
- c)27
- d)30
- e)Such a distribution is not possible
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A man distributed some chocolates among his three children A, B and C ...
Let x, y and z be the number of chocolates given to A, B and C respectively.
From the first condition,
z - 1 = x + y ⇒ x + y - z = -1 ...(i)
From the second condition,
x + z / 2 = y ⇒ x - 2y + z = 0 ..(ii)
From the third condition,
x + 2 / 3 y - 1 = 3 / 5(z + 1) = 1 / 3y + 2 / 5(z + 1)
∴ 15x + 10y - 15 = 9z + 9 and 9z + 9 = 5y + 6z + 6
i.e., 15x + 10y - 9z = 24 ..(iii)
and 5y - 3z = 3...(iv)
∴ Subtracting (ii) from (i); we get
⇒ 3y - 2z = 3 ...(v)
Solving (iv) and (v); we get y = 9, z = 14
From (i), we get x = 4 We can check that values of x, y and z satisfy equation (iii) x + y + z = 27 Hence, option 3.
From the first condition,
z - 1 = x + y ⇒ x + y - z = -1 ...(i)
From the second condition,
x + z / 2 = y ⇒ x - 2y + z = 0 ..(ii)
From the third condition,
x + 2 / 3 y - 1 = 3 / 5(z + 1) = 1 / 3y + 2 / 5(z + 1)
∴ 15x + 10y - 15 = 9z + 9 and 9z + 9 = 5y + 6z + 6
i.e., 15x + 10y - 9z = 24 ..(iii)
and 5y - 3z = 3...(iv)
∴ Subtracting (ii) from (i); we get
⇒ 3y - 2z = 3 ...(v)
Solving (iv) and (v); we get y = 9, z = 14
From (i), we get x = 4 We can check that values of x, y and z satisfy equation (iii) x + y + z = 27 Hence, option 3.
Most Upvoted Answer
A man distributed some chocolates among his three children A, B and C ...
Let's solve the problem step by step:
Step 1: Let's assume the number of chocolates distributed by the man is 'x'.
Step 2: As per the given condition, everyone gets at least 4 chocolates. So, we can write the equation as:
A + B + C = x
Step 3: According to the second condition, if one chocolate is taken back from C, then the total number of chocolates of A and B would be equal to that of C. So, we can write the equation as:
(A + B) = (C - 1)
Step 4: The number of chocolates of B is the average of the number of chocolates of A and C. So, we can write the equation as:
B = (A + C)/2
Step 5: According to the third condition, B gave 2/3rd of the number of chocolates he had to A. So, B is left with (1/3)rd of the number of chocolates he had. We can write the equation as:
B - (2/3)B = (1/3)B
Step 6: A gave one 2 chocolate to C. So, A is left with (A - 2) chocolates and C has (C + 1) chocolates. We can write the equation as:
A - 2 = C + 1
Step 7: According to the fourth condition, C gave 2/5th of the number of chocolates he then had to B. So, C is left with (3/5)th of the number of chocolates he had. We can write the equation as:
(3/5)C = B + (2/5)C
Step 8: According to the fifth condition, if all of them have an equal number of chocolates, then the number of chocolates for A, B, and C should be the same. So, we can equate all the equations we derived above.
Solving these equations simultaneously, we get:
A = 9, B = 12, C = 6
Step 9: Now, we need to find the value of x, which is the total number of chocolates distributed by the man. We can substitute the values of A, B, and C in the equation from Step 2:
9 + 12 + 6 = x
x = 27
Therefore, the man distributed 27 chocolates among his three children. Hence, the correct answer is option 'C'.
Step 1: Let's assume the number of chocolates distributed by the man is 'x'.
Step 2: As per the given condition, everyone gets at least 4 chocolates. So, we can write the equation as:
A + B + C = x
Step 3: According to the second condition, if one chocolate is taken back from C, then the total number of chocolates of A and B would be equal to that of C. So, we can write the equation as:
(A + B) = (C - 1)
Step 4: The number of chocolates of B is the average of the number of chocolates of A and C. So, we can write the equation as:
B = (A + C)/2
Step 5: According to the third condition, B gave 2/3rd of the number of chocolates he had to A. So, B is left with (1/3)rd of the number of chocolates he had. We can write the equation as:
B - (2/3)B = (1/3)B
Step 6: A gave one 2 chocolate to C. So, A is left with (A - 2) chocolates and C has (C + 1) chocolates. We can write the equation as:
A - 2 = C + 1
Step 7: According to the fourth condition, C gave 2/5th of the number of chocolates he then had to B. So, C is left with (3/5)th of the number of chocolates he had. We can write the equation as:
(3/5)C = B + (2/5)C
Step 8: According to the fifth condition, if all of them have an equal number of chocolates, then the number of chocolates for A, B, and C should be the same. So, we can equate all the equations we derived above.
Solving these equations simultaneously, we get:
A = 9, B = 12, C = 6
Step 9: Now, we need to find the value of x, which is the total number of chocolates distributed by the man. We can substitute the values of A, B, and C in the equation from Step 2:
9 + 12 + 6 = x
x = 27
Therefore, the man distributed 27 chocolates among his three children. Hence, the correct answer is option 'C'.
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A man distributed some chocolates among his three children A, B and C (everyone gets at least 4 chocolates). If the man took back one chocolate from C, the total number of chocolates of A and B would be equal to that of C. The number of chocolates ofB is the average of number of chocolates of A and C. If B gave2/3rdof the number of chocolates he had to A, A gave one 2 chocolate to C and then if C gave2/5thof the number of chocolates he then had to B, then all of them would have equal number of chocolates. How many chocolates did the man distribute?a)21b)24c)27d)30e)Such a distribution is not possibleCorrect answer is option 'C'. Can you explain this answer?
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A man distributed some chocolates among his three children A, B and C (everyone gets at least 4 chocolates). If the man took back one chocolate from C, the total number of chocolates of A and B would be equal to that of C. The number of chocolates ofB is the average of number of chocolates of A and C. If B gave2/3rdof the number of chocolates he had to A, A gave one 2 chocolate to C and then if C gave2/5thof the number of chocolates he then had to B, then all of them would have equal number of chocolates. How many chocolates did the man distribute?a)21b)24c)27d)30e)Such a distribution is not possibleCorrect answer is option 'C'. 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 man distributed some chocolates among his three children A, B and C (everyone gets at least 4 chocolates). If the man took back one chocolate from C, the total number of chocolates of A and B would be equal to that of C. The number of chocolates ofB is the average of number of chocolates of A and C. If B gave2/3rdof the number of chocolates he had to A, A gave one 2 chocolate to C and then if C gave2/5thof the number of chocolates he then had to B, then all of them would have equal number of chocolates. How many chocolates did the man distribute?a)21b)24c)27d)30e)Such a distribution is not possibleCorrect answer is option 'C'. 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 man distributed some chocolates among his three children A, B and C (everyone gets at least 4 chocolates). If the man took back one chocolate from C, the total number of chocolates of A and B would be equal to that of C. The number of chocolates ofB is the average of number of chocolates of A and C. If B gave2/3rdof the number of chocolates he had to A, A gave one 2 chocolate to C and then if C gave2/5thof the number of chocolates he then had to B, then all of them would have equal number of chocolates. How many chocolates did the man distribute?a)21b)24c)27d)30e)Such a distribution is not possibleCorrect answer is option 'C'. Can you explain this answer?.
A man distributed some chocolates among his three children A, B and C (everyone gets at least 4 chocolates). If the man took back one chocolate from C, the total number of chocolates of A and B would be equal to that of C. The number of chocolates ofB is the average of number of chocolates of A and C. If B gave2/3rdof the number of chocolates he had to A, A gave one 2 chocolate to C and then if C gave2/5thof the number of chocolates he then had to B, then all of them would have equal number of chocolates. How many chocolates did the man distribute?a)21b)24c)27d)30e)Such a distribution is not possibleCorrect answer is option 'C'. 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 man distributed some chocolates among his three children A, B and C (everyone gets at least 4 chocolates). If the man took back one chocolate from C, the total number of chocolates of A and B would be equal to that of C. The number of chocolates ofB is the average of number of chocolates of A and C. If B gave2/3rdof the number of chocolates he had to A, A gave one 2 chocolate to C and then if C gave2/5thof the number of chocolates he then had to B, then all of them would have equal number of chocolates. How many chocolates did the man distribute?a)21b)24c)27d)30e)Such a distribution is not possibleCorrect answer is option 'C'. 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 man distributed some chocolates among his three children A, B and C (everyone gets at least 4 chocolates). If the man took back one chocolate from C, the total number of chocolates of A and B would be equal to that of C. The number of chocolates ofB is the average of number of chocolates of A and C. If B gave2/3rdof the number of chocolates he had to A, A gave one 2 chocolate to C and then if C gave2/5thof the number of chocolates he then had to B, then all of them would have equal number of chocolates. How many chocolates did the man distribute?a)21b)24c)27d)30e)Such a distribution is not possibleCorrect answer is option 'C'. Can you explain this answer?.
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A man distributed some chocolates among his three children A, B and C (everyone gets at least 4 chocolates). If the man took back one chocolate from C, the total number of chocolates of A and B would be equal to that of C. The number of chocolates ofB is the average of number of chocolates of A and C. If B gave2/3rdof the number of chocolates he had to A, A gave one 2 chocolate to C and then if C gave2/5thof the number of chocolates he then had to B, then all of them would have equal number of chocolates. How many chocolates did the man distribute?a)21b)24c)27d)30e)Such a distribution is not possibleCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A man distributed some chocolates among his three children A, B and C (everyone gets at least 4 chocolates). If the man took back one chocolate from C, the total number of chocolates of A and B would be equal to that of C. The number of chocolates ofB is the average of number of chocolates of A and C. If B gave2/3rdof the number of chocolates he had to A, A gave one 2 chocolate to C and then if C gave2/5thof the number of chocolates he then had to B, then all of them would have equal number of chocolates. How many chocolates did the man distribute?a)21b)24c)27d)30e)Such a distribution is not possibleCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A man distributed some chocolates among his three children A, B and C (everyone gets at least 4 chocolates). If the man took back one chocolate from C, the total number of chocolates of A and B would be equal to that of C. The number of chocolates ofB is the average of number of chocolates of A and C. If B gave2/3rdof the number of chocolates he had to A, A gave one 2 chocolate to C and then if C gave2/5thof the number of chocolates he then had to B, then all of them would have equal number of chocolates. How many chocolates did the man distribute?a)21b)24c)27d)30e)Such a distribution is not possibleCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A man distributed some chocolates among his three children A, B and C (everyone gets at least 4 chocolates). If the man took back one chocolate from C, the total number of chocolates of A and B would be equal to that of C. The number of chocolates ofB is the average of number of chocolates of A and C. If B gave2/3rdof the number of chocolates he had to A, A gave one 2 chocolate to C and then if C gave2/5thof the number of chocolates he then had to B, then all of them would have equal number of chocolates. How many chocolates did the man distribute?a)21b)24c)27d)30e)Such a distribution is not possibleCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice CAT tests.
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