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A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor? A. 13 B. 59 C. 35 D. 37 E. 12 F. NoA?
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A number when divided by a divisor leaves a remainder of 24. When twic...
Problem: A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
Solution:
Let's assume the number to be 'x' and the divisor to be 'd'.
According to the problem:
x = qd + 24 -------- (1) (where 'q' is the quotient)
2x = pd + 11 -------- (2) (where 'p' is the quotient)
Finding the value of 'x' using equation (1):
x = qd + 24
Therefore, x - 24 = qd
Finding the value of '2x' using equation (2):
2x = pd + 11
Substituting the value of 'x' from equation (1)
2(qd + 24) = pd + 11
2qd + 48 = pd + 11
pd - 2qd = 37
Finding the value of 'd' using the above two equations:
pd - 2qd = 37
d(p - 2q) = 37
As 37 is a prime number, the value of 'd' can be 1 and 37 only.
When d = 1, p - 2q = 37, which is not possible as it would require 'p' and 'q' to be negative.
Therefore, d = 37.
Hence, the value of the divisor is 37. (Option D)
Solution:
Let's assume the number to be 'x' and the divisor to be 'd'.
According to the problem:
x = qd + 24 -------- (1) (where 'q' is the quotient)
2x = pd + 11 -------- (2) (where 'p' is the quotient)
Finding the value of 'x' using equation (1):
x = qd + 24
Therefore, x - 24 = qd
Finding the value of '2x' using equation (2):
2x = pd + 11
Substituting the value of 'x' from equation (1)
2(qd + 24) = pd + 11
2qd + 48 = pd + 11
pd - 2qd = 37
Finding the value of 'd' using the above two equations:
pd - 2qd = 37
d(p - 2q) = 37
As 37 is a prime number, the value of 'd' can be 1 and 37 only.
When d = 1, p - 2q = 37, which is not possible as it would require 'p' and 'q' to be negative.
Therefore, d = 37.
Hence, the value of the divisor is 37. (Option D)
Community Answer
A number when divided by a divisor leaves a remainder of 24. When twic...
Let the original number be 'a'
Let the divisor be 'd'
Let the quotient of the division of a by d be 'x'
Therefore, we can write the relation as a/d=x and the remainder is 24.
i.e., a=dx+24
When twice the original number is divided by d,2a is divided by d.
We know that a=dx+24. Therefore, 2a=2dx+48
The problem states that (2dx+48)/d leaves a remainder of 11.
2dx is perfectly divisible by d and will, therefore, not leave a remainder.
The remainder of 11 was obtained by dividing 48 by d.
When 48 is divided by 37, the remainder that one will obtain is 11.
Hence, the divisor is 37.
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A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor? A. 13 B. 59 C. 35 D. 37 E. 12 F. NoA?
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A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor? A. 13 B. 59 C. 35 D. 37 E. 12 F. NoA? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor? A. 13 B. 59 C. 35 D. 37 E. 12 F. NoA? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor? A. 13 B. 59 C. 35 D. 37 E. 12 F. NoA?.
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