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The ratio of the two numbers is 11 : 4 and the H.C.F is 16, then find the sum of the two numbers.
- a)240
- b)255
- c)480
- d)220
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The ratio of the two numbers is 11 : 4 and the H.C.F is 16, then find ...
Given:
The ratio of the two numbers is 11 : 4.
The H.C.F is 16
Concept used:
(1) For the two numbers in the ratio y : z.
The value of first number = H.C.F × y
The value of first number = H.C.F × z
Calculation:
The value of first number = 16 × 11 = 176
The value of second number = 16 × 4 = 64
The required sum = 176 + 64 = 240
∴ The required answer is 240.
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Community Answer
The ratio of the two numbers is 11 : 4 and the H.C.F is 16, then find ...
Given Information:
- The ratio of the two numbers is 11:4.
- The highest common factor (H.C.F) of the two numbers is 16.
Approach:
To find the sum of the two numbers, we first need to determine their individual values. We can do this by using the given ratio and the H.C.F.
Step 1: Determine the Multiples
- Let the two numbers be 11x and 4x, where x is a common factor.
- As the H.C.F is 16, it means that x must be a multiple of 16. So, let's assume x = 16n, where n is a positive integer.
Step 2: Calculate the Sum
- The sum of the two numbers is given by 11x + 4x = 15x.
- Substituting x = 16n, we have 15x = 15(16n) = 240n.
Conclusion:
The sum of the two numbers is 240n. Since n can be any positive integer, the sum can take multiple values, all of which are multiples of 240. Therefore, the correct answer is option A, 240.
- The ratio of the two numbers is 11:4.
- The highest common factor (H.C.F) of the two numbers is 16.
Approach:
To find the sum of the two numbers, we first need to determine their individual values. We can do this by using the given ratio and the H.C.F.
Step 1: Determine the Multiples
- Let the two numbers be 11x and 4x, where x is a common factor.
- As the H.C.F is 16, it means that x must be a multiple of 16. So, let's assume x = 16n, where n is a positive integer.
Step 2: Calculate the Sum
- The sum of the two numbers is given by 11x + 4x = 15x.
- Substituting x = 16n, we have 15x = 15(16n) = 240n.
Conclusion:
The sum of the two numbers is 240n. Since n can be any positive integer, the sum can take multiple values, all of which are multiples of 240. Therefore, the correct answer is option A, 240.
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