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The LCM of two number is 45 times their HCF. If one of the numbers is 125 and the sum of HCF and LCM is 1150, the other number is:
- a)215
- b)220
- c)225
- d)235
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The LCM of two number is 45 times their HCF. If one of the numbers is ...
Let the lcm be x and hcf be y and the other number be z.
Given lcm of 2 numbers is 45 times their hcf, the sum of HCF + LCM is 1150.
y = 45x. ---- (1)
x + y = 1150 --- (2)
Substitute equation (1) in (2), we get
46x = 1150
x = 25.
Substitute x = 25 in (1), we get
y = 45 * 25 = 1125.
We know that product of two numbers = LCM * HCF
125 * z = 25 * 1125
z = 25 * 1125/125
= 225.
The other number = 225.
Most Upvoted Answer
The LCM of two number is 45 times their HCF. If one of the numbers is ...
Given information:
- LCM of two numbers = 45 times their HCF
- One number = 125
- Sum of HCF and LCM = 1150
To find:
- Other number
Solution:
Step 1: Let the other number be x.
Step 2: HCF of 125 and x = h (let's assume)
Step 3: LCM of 125 and x = 125x/h (using formula HCF x LCM = Product of two numbers)
Step 4: Given, LCM of 125 and x = 45h
=> 125x/h = 45h
=> x = 45h^2/125 ---(Equation 1)
Step 5: Sum of HCF and LCM = 125x/h + h = 1150
=> 125x + h^2 = 1150h
=> 125x = 1150h - h^2
=> x = (1150h - h^2)/125 ---(Equation 2)
Equating Equation 1 and Equation 2, we get:
45h^2/125 = (1150h - h^2)/125
=> 45h^2 = 1150h - h^2
=> 46h^2 = 1150h
=> h = 25
Substituting h = 25 in Equation 1, we get:
x = 45h^2/125
=> x = 45*25^2/125
=> x = 225
Therefore, the other number is 225.
Hence, option (c) is the correct answer.
- LCM of two numbers = 45 times their HCF
- One number = 125
- Sum of HCF and LCM = 1150
To find:
- Other number
Solution:
Step 1: Let the other number be x.
Step 2: HCF of 125 and x = h (let's assume)
Step 3: LCM of 125 and x = 125x/h (using formula HCF x LCM = Product of two numbers)
Step 4: Given, LCM of 125 and x = 45h
=> 125x/h = 45h
=> x = 45h^2/125 ---(Equation 1)
Step 5: Sum of HCF and LCM = 125x/h + h = 1150
=> 125x + h^2 = 1150h
=> 125x = 1150h - h^2
=> x = (1150h - h^2)/125 ---(Equation 2)
Equating Equation 1 and Equation 2, we get:
45h^2/125 = (1150h - h^2)/125
=> 45h^2 = 1150h - h^2
=> 46h^2 = 1150h
=> h = 25
Substituting h = 25 in Equation 1, we get:
x = 45h^2/125
=> x = 45*25^2/125
=> x = 225
Therefore, the other number is 225.
Hence, option (c) is the correct answer.
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The LCM of two number is 45 times their HCF. If one of the numbers is 125 and the sum of HCF and LCM is 1150, the other number is:a)215b)220c)225d)235Correct answer is option 'C'. Can you explain this answer?
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The LCM of two number is 45 times their HCF. If one of the numbers is 125 and the sum of HCF and LCM is 1150, the other number is:a)215b)220c)225d)235Correct answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The LCM of two number is 45 times their HCF. If one of the numbers is 125 and the sum of HCF and LCM is 1150, the other number is:a)215b)220c)225d)235Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The LCM of two number is 45 times their HCF. If one of the numbers is 125 and the sum of HCF and LCM is 1150, the other number is:a)215b)220c)225d)235Correct answer is option 'C'. Can you explain this answer?.
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