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Two natural numbers are in the ratio 3 : 5 and their product is 2160. The smallest of the number is
- a)36
- b)24
- c)18
- d)12
Correct answer is option 'A'. Can you explain this answer?
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Two natural numbers are in the ratio 3 : 5 and their product is 2160. ...
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Two natural numbers are in the ratio 3 : 5 and their product is 2160. ...
Given information:
- The ratio of two natural numbers is 3:5.
- The product of these two numbers is 2160.
Let's solve the problem step by step:
Step 1: Determining the ratio
- The given ratio is 3:5.
- This means that one number is 3 times smaller than the other number.
- Let's assume the smaller number as 3x and the larger number as 5x.
Step 2: Determining the product
- The product of the two numbers is 2160.
- This means that (3x) * (5x) = 2160.
- Simplifying the equation, we get 15x^2 = 2160.
- Dividing both sides of the equation by 15, we get x^2 = 144.
- Taking the square root on both sides, we get x = 12.
Step 3: Finding the smaller number
- We assumed the smaller number as 3x.
- Substituting the value of x, we get 3 * 12 = 36.
Conclusion:
- The smaller number is 36, which is option A.
- The ratio of two natural numbers is 3:5.
- The product of these two numbers is 2160.
Let's solve the problem step by step:
Step 1: Determining the ratio
- The given ratio is 3:5.
- This means that one number is 3 times smaller than the other number.
- Let's assume the smaller number as 3x and the larger number as 5x.
Step 2: Determining the product
- The product of the two numbers is 2160.
- This means that (3x) * (5x) = 2160.
- Simplifying the equation, we get 15x^2 = 2160.
- Dividing both sides of the equation by 15, we get x^2 = 144.
- Taking the square root on both sides, we get x = 12.
Step 3: Finding the smaller number
- We assumed the smaller number as 3x.
- Substituting the value of x, we get 3 * 12 = 36.
Conclusion:
- The smaller number is 36, which is option A.
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