The LCM of two numbers is 40 and their HCF is 4. If the difference between the two numbers is 12, then the sum of the numbers is || ADRE 1.0 SLRC 2022 PAPER-III SOLVED QUESTIONS
The LCM of two numbers is 40 and their HCF is 4. If the difference between the two numbers is 12, then the sum of the numbers is:
(A) 20
(B) 24
(C) 28
(D) 32
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Solution:
Given:
- LCM of two numbers = 40
- HCF of two numbers = 4
- Difference between the two numbers = 12
Let, the two numbers be a and b
Using the relationship between LCM and HCF:
a×b=LCM×HCF
a×b=40×4
a×b=160
Let the two numbers be 4x and 4y where x and y are coprime integers (since their HCF is 1).
Thus:
4x × 4y=160
xy=10
Also, the difference between the two numbers:
∣4x−4y∣=12
4∣x−y∣=12
∣x−y∣=3
So, we need to find pairs (x,y) that satisfy xy=10 and ∣x−y∣=3.
Possible pairs:
x=5 and y=2 (since 5×2=10 and ∣5−2∣=3)
Let's calculate the actual numbers:
a=4x=4×5=20
b=4y=4×2=8
The sum of the numbers:
a+b=20+8=28
Therefore, the sum of the numbers is 28.
Answer: (C) 28
Why this problem is important?
- Fundamental Math Skills: Enhances understanding of LCM, HCF, and their relationship, which is essential for solving various mathematical problems.
- Competitive Exam Relevance: Frequently tested in competitive exams like ADRE's SLRC-2022 Paper-III, making it crucial for exam preparation.
- Problem-solving Practice: Develops logical thinking and problem-solving skills, which are vital for tackling complex questions in exams.
Now it's okay, but during exams, I forget everything! 😂
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