Software Development Exam > Software Development Questions > Two numbers are in the ratio 12 : 7. If their...
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Two numbers are in the ratio 12 : 7. If their HCF is 25, find the numbers.
- a)225, 135
- b)300, 175
- c)300, 50
- d)175, 120
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Two numbers are in the ratio 12 : 7. If their HCF is 25, find the numb...
Given:
Ratio of two numbers = 12 : 7
HCF = 25
Formula:
Numbers = (HCF
×
Ratio part)Solution:
First number = 25 × 12 = 300
Second number = 25
×
7 = 175Numbers are 300 and 175.
Most Upvoted Answer
Two numbers are in the ratio 12 : 7. If their HCF is 25, find the numb...
Given Ratio and HCF
The given ratio of the two numbers is 12:7, and their highest common factor (HCF) is 25.
Expressing the Numbers
Let's assume the numbers are 12x and 7x, where x is a common factor of the two numbers.
Using HCF to Find x
Since the HCF of the numbers is 25, we can write:
25 = HCF = gcd(12x, 7x)
This implies that x = 25.
Finding the Actual Numbers
Substitute x = 25 back into the expressions for the numbers:
First number = 12x = 12 * 25 = 300
Second number = 7x = 7 * 25 = 175
Therefore, the numbers are 300 and 175, which matches option B.
The given ratio of the two numbers is 12:7, and their highest common factor (HCF) is 25.
Expressing the Numbers
Let's assume the numbers are 12x and 7x, where x is a common factor of the two numbers.
Using HCF to Find x
Since the HCF of the numbers is 25, we can write:
25 = HCF = gcd(12x, 7x)
This implies that x = 25.
Finding the Actual Numbers
Substitute x = 25 back into the expressions for the numbers:
First number = 12x = 12 * 25 = 300
Second number = 7x = 7 * 25 = 175
Therefore, the numbers are 300 and 175, which matches option B.
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Two numbers are in the ratio 12 : 7. If their HCF is 25, find the numbers.a)225, 135b)300, 175c)300, 50 d)175, 120Correct answer is option 'B'. Can you explain this answer?
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