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The ratio of two numbers is 1 ∶ 5 and their product is 320. What is the difference between the squares of these two numbers?
- a)1024
- b)1256
- c)1536
- d)1640
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The ratio of two numbers is 1 5 and their product is 320. What is the...
The ratio of two numbers is 1 ∶ 5 and their product is 320;
Suppose the numbers are x and 5x;
∴ x × 5x = 320
⇒ 5x2 = 320
⇒ x2 = 64
⇒ x = 8
∴ The numbers are 8 and 40;
∴ Difference between the squares of these two numbers = 1600 – 64 = 1536
Suppose the numbers are x and 5x;
∴ x × 5x = 320
⇒ 5x2 = 320
⇒ x2 = 64
⇒ x = 8
∴ The numbers are 8 and 40;
∴ Difference between the squares of these two numbers = 1600 – 64 = 1536
Most Upvoted Answer
The ratio of two numbers is 1 5 and their product is 320. What is the...
Ratio of the numbers: 1:5
Product of the numbers: 320
To find the difference between the squares of the two numbers, we need to determine the individual values of the numbers.
Let's assume the two numbers are x and y, where x is the smaller number and y is the larger number.
Given that the ratio of the numbers is 1:5, we can write the equation:
x/y = 1/5
Cross-multiplying, we get:
5x = y
We are also given that the product of the numbers is 320, so we can write the equation:
xy = 320
Now, we have a system of equations:
5x = y ...(1)
xy = 320 ...(2)
Solving these equations to find the values of x and y:
Substituting the value of y from equation (1) into equation (2):
x(5x) = 320
5x^2 = 320
x^2 = 320/5
x^2 = 64
x = √64
x = 8
Substituting the value of x into equation (1):
5(8) = y
y = 40
So, the two numbers are 8 and 40.
Now, we can find the difference between the squares of these two numbers:
Difference between the squares of the numbers: (y^2) - (x^2)
= (40^2) - (8^2)
= 1600 - 64
= 1536
Therefore, the difference between the squares of the two numbers is 1536. Hence, option C is the correct answer.
Product of the numbers: 320
To find the difference between the squares of the two numbers, we need to determine the individual values of the numbers.
Let's assume the two numbers are x and y, where x is the smaller number and y is the larger number.
Given that the ratio of the numbers is 1:5, we can write the equation:
x/y = 1/5
Cross-multiplying, we get:
5x = y
We are also given that the product of the numbers is 320, so we can write the equation:
xy = 320
Now, we have a system of equations:
5x = y ...(1)
xy = 320 ...(2)
Solving these equations to find the values of x and y:
Substituting the value of y from equation (1) into equation (2):
x(5x) = 320
5x^2 = 320
x^2 = 320/5
x^2 = 64
x = √64
x = 8
Substituting the value of x into equation (1):
5(8) = y
y = 40
So, the two numbers are 8 and 40.
Now, we can find the difference between the squares of these two numbers:
Difference between the squares of the numbers: (y^2) - (x^2)
= (40^2) - (8^2)
= 1600 - 64
= 1536
Therefore, the difference between the squares of the two numbers is 1536. Hence, option C is the correct answer.
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Community Answer
The ratio of two numbers is 1 5 and their product is 320. What is the...
The ratio of two numbers is 1 ∶ 5 and their product is 320;
Suppose the numbers are x and 5x;
∴ x × 5x = 320
⇒ 5x2 = 320
⇒ x2 = 64
⇒ x = 8
∴ The numbers are 8 and 40;
∴ Difference between the squares of these two numbers = 1600 – 64 = 1536
Suppose the numbers are x and 5x;
∴ x × 5x = 320
⇒ 5x2 = 320
⇒ x2 = 64
⇒ x = 8
∴ The numbers are 8 and 40;
∴ Difference between the squares of these two numbers = 1600 – 64 = 1536
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The ratio of two numbers is 1 5 and their product is 320. What is the difference between the squares of these two numbers?a)1024b)1256c)1536d)1640Correct answer is option 'C'. Can you explain this answer?
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