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There are two numbers whose sum is 250 and difference of their squares is 9000. Find the larger number ?
- a)97
- b)107
- c)143
- d)123
Correct answer is option 'C'. Can you explain this answer?
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There are two numbers whose sum is 250 and difference of their squares...
So the answer is option C.
Most Upvoted Answer
There are two numbers whose sum is 250 and difference of their squares...
Question Analysis:
We are given two conditions in the question:
1) The sum of two numbers is 250.
2) The difference of their squares is 9000.
Let's assume the two numbers as x and y:
According to the first condition, the sum of x and y is 250.
So, we can write the equation as:
x + y = 250
According to the second condition, the difference of their squares is 9000.
So, we can write the equation as:
x^2 - y^2 = 9000
Now, let's solve these equations to find the values of x and y.
Solving the equations:
We can rewrite the first equation as:
x = 250 - y
Substituting this value of x in the second equation, we get:
(250 - y)^2 - y^2 = 9000
Expanding the equation, we get:
62500 - 500y + y^2 - y^2 = 9000
Simplifying further, we get:
-500y = 9000 - 62500
-500y = -53500
Dividing both sides by -500, we get:
y = 107
Substituting this value of y in the first equation, we get:
x + 107 = 250
x = 250 - 107
x = 143
Conclusion:
The larger number is 143, which is option C.
We are given two conditions in the question:
1) The sum of two numbers is 250.
2) The difference of their squares is 9000.
Let's assume the two numbers as x and y:
According to the first condition, the sum of x and y is 250.
So, we can write the equation as:
x + y = 250
According to the second condition, the difference of their squares is 9000.
So, we can write the equation as:
x^2 - y^2 = 9000
Now, let's solve these equations to find the values of x and y.
Solving the equations:
We can rewrite the first equation as:
x = 250 - y
Substituting this value of x in the second equation, we get:
(250 - y)^2 - y^2 = 9000
Expanding the equation, we get:
62500 - 500y + y^2 - y^2 = 9000
Simplifying further, we get:
-500y = 9000 - 62500
-500y = -53500
Dividing both sides by -500, we get:
y = 107
Substituting this value of y in the first equation, we get:
x + 107 = 250
x = 250 - 107
x = 143
Conclusion:
The larger number is 143, which is option C.
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There are two numbers whose sum is 250 and difference of their squares is 9000. Find the larger number ?a)97b)107c)143d)123Correct answer is option 'C'. Can you explain this answer?
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