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The difference between two numbers is 22 and their product is 240, what is the difference between their reciprocals ?
- a)11/120
- b)-11/120
- c)11/109
- d)-11/109
Correct answer is option 'B'. Can you explain this answer?
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The difference between two numbers is 22 and their product is 240, wha...
p – q = 22, pq = 240.
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The difference between two numbers is 22 and their product is 240, wha...
Given: Difference between two numbers = 22 and their product = 240
Let the two numbers be x and y, where x>y.
From the given information, we can form the following equations:
x - y = 22 ...(1) (as the difference between the numbers is 22)
x*y = 240 ...(2) (as their product is 240)
Solving equation (1) for x, we get:
x = y + 22
Substituting this value of x in equation (2), we get:
(y + 22)*y = 240
Expanding the above equation, we get:
y^2 + 22y - 240 = 0
This is a quadratic equation in y, which can be solved using factorization or the quadratic formula. On solving, we get:
y = 8 or y = -30
Since x>y, we take y = 8 and x = 30.
Therefore, the two numbers are 30 and 8.
Now, we need to find the difference between their reciprocals:
1/x - 1/y = (y - x)/(xy)
Substituting the values of x and y, we get:
1/30 - 1/8 = (8 - 30)/(240)
= -22/240
= -11/120
Therefore, the difference between their reciprocals is -11/120.
Hence, the correct option is (b) -11/120.
Let the two numbers be x and y, where x>y.
From the given information, we can form the following equations:
x - y = 22 ...(1) (as the difference between the numbers is 22)
x*y = 240 ...(2) (as their product is 240)
Solving equation (1) for x, we get:
x = y + 22
Substituting this value of x in equation (2), we get:
(y + 22)*y = 240
Expanding the above equation, we get:
y^2 + 22y - 240 = 0
This is a quadratic equation in y, which can be solved using factorization or the quadratic formula. On solving, we get:
y = 8 or y = -30
Since x>y, we take y = 8 and x = 30.
Therefore, the two numbers are 30 and 8.
Now, we need to find the difference between their reciprocals:
1/x - 1/y = (y - x)/(xy)
Substituting the values of x and y, we get:
1/30 - 1/8 = (8 - 30)/(240)
= -22/240
= -11/120
Therefore, the difference between their reciprocals is -11/120.
Hence, the correct option is (b) -11/120.
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