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The ratio of two numbers is 5: 7. If 7 is added to the first number and 10 is subtracted from the second number, then the new ratio is 3: 2, then find the sum of the squares of the two numbers.
- a)74
- b)1184
- c)13
- d)52
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The ratio of two numbers is 5: 7. If 7 is added to the first number a...
Let the number be 5x and 7x,
View all questions of this test
So 
x Solving for, we get 'x' = 4
Hence, the numbers are 20 and 28
the sum of the squares of the two numbers = 1184
Hence, the correct option is (B)
Most Upvoted Answer
The ratio of two numbers is 5: 7. If 7 is added to the first number a...
Given:
The ratio of two numbers is 5:7.
Let's assume:
Let the two numbers be 5x and 7x, where x is a constant.
First scenario:
When 7 is added to the first number and 10 is subtracted from the second number.
So, the new numbers are (5x + 7) and (7x - 10).
New ratio:
The new ratio is given as 3:2.
So, (5x + 7)/(7x - 10) = 3/2.
Solving the equation:
Cross multiplying, we get:
2(5x + 7) = 3(7x - 10).
Simplifying further, we get:
10x + 14 = 21x - 30.
Bringing all the x terms to one side and all the constant terms to the other side, we get:
21x - 10x = 14 + 30.
Simplifying further, we get:
11x = 44.
Dividing both sides by 11, we get:
x = 4.
Calculating the numbers:
The first number = 5x = 5(4) = 20.
The second number = 7x = 7(4) = 28.
Calculating the sum of squares:
The sum of squares = (20^2) + (28^2) = 400 + 784 = <400+784=1184>>1184.
Therefore, the correct answer is option B) 1184.
The ratio of two numbers is 5:7.
Let's assume:
Let the two numbers be 5x and 7x, where x is a constant.
First scenario:
When 7 is added to the first number and 10 is subtracted from the second number.
So, the new numbers are (5x + 7) and (7x - 10).
New ratio:
The new ratio is given as 3:2.
So, (5x + 7)/(7x - 10) = 3/2.
Solving the equation:
Cross multiplying, we get:
2(5x + 7) = 3(7x - 10).
Simplifying further, we get:
10x + 14 = 21x - 30.
Bringing all the x terms to one side and all the constant terms to the other side, we get:
21x - 10x = 14 + 30.
Simplifying further, we get:
11x = 44.
Dividing both sides by 11, we get:
x = 4.
Calculating the numbers:
The first number = 5x = 5(4) = 20.
The second number = 7x = 7(4) = 28.
Calculating the sum of squares:
The sum of squares = (20^2) + (28^2) = 400 + 784 = <400+784=1184>>1184.
Therefore, the correct answer is option B) 1184.
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The ratio of two numbers is 5: 7. If 7 is added to the first number and 10 is subtracted from the second number, then the new ratio is 3: 2, then find the sum of the squares of the two numbers.a)74b)1184c)13d)52Correct answer is option 'B'. Can you explain this answer?
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