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Rahul's roll number in lES Exam is a number consisting of three non-zero distinct digits, such that the sum of the digits at hundreds and unit’s place is equal to that half of the digit at ten’s place. Also the sum of all possible three digit numbers obtained using these three digits without repetition is 2664.
Q. The digits in the tens given is
- a)6
- b)8
- c)9
- d)2
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
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Let the digits be a. y. z such that the number is 106r + 10y + z
View all questions of this test
Thus, the omer rive 3 digit number which we may obtained using these 3 digits will be
100x + 10z + y
100y + 10x + z
100y + 10z + x
100z + 10x + y
100z + 10y + x
Now when we add ail the six three digit numbers possible to be formed by these three digits:
222 (x + y + z) = 2664 or x + y + z = 12
Also x + z = y/2 thus y = 8
Thus, x + z = 4
As the digits are non zero and distinct thus x and z have to be 1 and 3 but not necessarily in the same order. Thus we cannot say whether the number is 183 or 381.
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Question: What is the digit in the tens place of Rahul's roll number in LES Exam?
Given Information:
- Rahul's roll number is a number consisting of three non-zero distinct digits.
- The sum of the digits at hundreds and unit’s place is equal to that half of the digit at ten’s place.
- The sum of all possible three digit numbers obtained using these three digits without repetition is 2664.
Solution:
Let's assume the digits in Rahul's roll number are a, b, and c. Then, we can write the following equations based on the given information:
- a, b, and c are three non-zero distinct digits.
- a + b = c/2
- The sum of all possible three digit numbers obtained using these three digits without repetition is 2664.
Using the third equation, we can find the sum of all possible combinations of a, b, and c:
(a + b + c) + (a + c + b) + (b + a + c) + (b + c + a) + (c + a + b) + (c + b + a) = 2664
Simplifying the equation, we get:
2(a + b + c) = 2664
a + b + c = 1332
Now, we can substitute the second equation in terms of c in the third equation:
a + b + (2a + 2b) = 1332
3a + 3b = 1332
a + b = 444
We can solve these equations to find the values of a, b, and c:
a + b = 444
a + b = c/2
c = 2(a + b)
Substituting the value of c in terms of a and b:
2(a + b) = 2a + 2b + c
c = 2(a + b) - 2a - 2b
c = 2(b - a)
As c is a non-zero digit, b must be greater than a. The possible values of (a, b) are:
(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (4, 5), (4, 6), (4, 7), (4, 8), (5, 6), (5, 7), (5, 8), (6, 7), (6, 8), (7, 8)
We can find the corresponding values of c for each pair of (a, b):
c = 2(b - a)
Adding all the possible values of c, we get:
2 + 4 + 6 + 8 + 10 + 12 + 14 + 4 + 6 + 8 + 10 + 12 + 14 + 6 + 8 +
Given Information:
- Rahul's roll number is a number consisting of three non-zero distinct digits.
- The sum of the digits at hundreds and unit’s place is equal to that half of the digit at ten’s place.
- The sum of all possible three digit numbers obtained using these three digits without repetition is 2664.
Solution:
Let's assume the digits in Rahul's roll number are a, b, and c. Then, we can write the following equations based on the given information:
- a, b, and c are three non-zero distinct digits.
- a + b = c/2
- The sum of all possible three digit numbers obtained using these three digits without repetition is 2664.
Using the third equation, we can find the sum of all possible combinations of a, b, and c:
(a + b + c) + (a + c + b) + (b + a + c) + (b + c + a) + (c + a + b) + (c + b + a) = 2664
Simplifying the equation, we get:
2(a + b + c) = 2664
a + b + c = 1332
Now, we can substitute the second equation in terms of c in the third equation:
a + b + (2a + 2b) = 1332
3a + 3b = 1332
a + b = 444
We can solve these equations to find the values of a, b, and c:
a + b = 444
a + b = c/2
c = 2(a + b)
Substituting the value of c in terms of a and b:
2(a + b) = 2a + 2b + c
c = 2(a + b) - 2a - 2b
c = 2(b - a)
As c is a non-zero digit, b must be greater than a. The possible values of (a, b) are:
(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (4, 5), (4, 6), (4, 7), (4, 8), (5, 6), (5, 7), (5, 8), (6, 7), (6, 8), (7, 8)
We can find the corresponding values of c for each pair of (a, b):
c = 2(b - a)
Adding all the possible values of c, we get:
2 + 4 + 6 + 8 + 10 + 12 + 14 + 4 + 6 + 8 + 10 + 12 + 14 + 6 + 8 +
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Direction : Read the following Information carefully and answer the question below it.Rahul's roll number in lES Exam is a number consisting of three non-zero distinct digits, such that the sum of the digits at hundreds and unit’s place is equal to that half of the digit at ten’s place. Also the sum of all possible three digit numbers obtained using these three digits without repetition is 2664.Q. The digits in the tens given isa)6b)8c)9d)2Correct answer is option 'B'. Can you explain this answer?
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Direction : Read the following Information carefully and answer the question below it.Rahul's roll number in lES Exam is a number consisting of three non-zero distinct digits, such that the sum of the digits at hundreds and unit’s place is equal to that half of the digit at ten’s place. Also the sum of all possible three digit numbers obtained using these three digits without repetition is 2664.Q. The digits in the tens given isa)6b)8c)9d)2Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Direction : Read the following Information carefully and answer the question below it.Rahul's roll number in lES Exam is a number consisting of three non-zero distinct digits, such that the sum of the digits at hundreds and unit’s place is equal to that half of the digit at ten’s place. Also the sum of all possible three digit numbers obtained using these three digits without repetition is 2664.Q. The digits in the tens given isa)6b)8c)9d)2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction : Read the following Information carefully and answer the question below it.Rahul's roll number in lES Exam is a number consisting of three non-zero distinct digits, such that the sum of the digits at hundreds and unit’s place is equal to that half of the digit at ten’s place. Also the sum of all possible three digit numbers obtained using these three digits without repetition is 2664.Q. The digits in the tens given isa)6b)8c)9d)2Correct answer is option 'B'. Can you explain this answer?.
Direction : Read the following Information carefully and answer the question below it.Rahul's roll number in lES Exam is a number consisting of three non-zero distinct digits, such that the sum of the digits at hundreds and unit’s place is equal to that half of the digit at ten’s place. Also the sum of all possible three digit numbers obtained using these three digits without repetition is 2664.Q. The digits in the tens given isa)6b)8c)9d)2Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Direction : Read the following Information carefully and answer the question below it.Rahul's roll number in lES Exam is a number consisting of three non-zero distinct digits, such that the sum of the digits at hundreds and unit’s place is equal to that half of the digit at ten’s place. Also the sum of all possible three digit numbers obtained using these three digits without repetition is 2664.Q. The digits in the tens given isa)6b)8c)9d)2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction : Read the following Information carefully and answer the question below it.Rahul's roll number in lES Exam is a number consisting of three non-zero distinct digits, such that the sum of the digits at hundreds and unit’s place is equal to that half of the digit at ten’s place. Also the sum of all possible three digit numbers obtained using these three digits without repetition is 2664.Q. The digits in the tens given isa)6b)8c)9d)2Correct answer is option 'B'. Can you explain this answer?.
Solutions for Direction : Read the following Information carefully and answer the question below it.Rahul's roll number in lES Exam is a number consisting of three non-zero distinct digits, such that the sum of the digits at hundreds and unit’s place is equal to that half of the digit at ten’s place. Also the sum of all possible three digit numbers obtained using these three digits without repetition is 2664.Q. The digits in the tens given isa)6b)8c)9d)2Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Direction : Read the following Information carefully and answer the question below it.Rahul's roll number in lES Exam is a number consisting of three non-zero distinct digits, such that the sum of the digits at hundreds and unit’s place is equal to that half of the digit at ten’s place. Also the sum of all possible three digit numbers obtained using these three digits without repetition is 2664.Q. The digits in the tens given isa)6b)8c)9d)2Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Direction : Read the following Information carefully and answer the question below it.Rahul's roll number in lES Exam is a number consisting of three non-zero distinct digits, such that the sum of the digits at hundreds and unit’s place is equal to that half of the digit at ten’s place. Also the sum of all possible three digit numbers obtained using these three digits without repetition is 2664.Q. The digits in the tens given isa)6b)8c)9d)2Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Direction : Read the following Information carefully and answer the question below it.Rahul's roll number in lES Exam is a number consisting of three non-zero distinct digits, such that the sum of the digits at hundreds and unit’s place is equal to that half of the digit at ten’s place. Also the sum of all possible three digit numbers obtained using these three digits without repetition is 2664.Q. The digits in the tens given isa)6b)8c)9d)2Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Direction : Read the following Information carefully and answer the question below it.Rahul's roll number in lES Exam is a number consisting of three non-zero distinct digits, such that the sum of the digits at hundreds and unit’s place is equal to that half of the digit at ten’s place. Also the sum of all possible three digit numbers obtained using these three digits without repetition is 2664.Q. The digits in the tens given isa)6b)8c)9d)2Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
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