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The sum of two numbers is 40 and their product is 375. What will be the sum of their reciprocals ?
Answer & Solution
Correct Answer:
Option
B
Let the numbers be x and y
Then,
x + y = 40 and xy = 375
$$\eqalign{ & \therefore \frac{1}{x} + \frac{1}{y} = \frac{{x + y}}{{xy}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{40}}{{275}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{8}{{75}} \cr} $$
Then,
x + y = 40 and xy = 375
$$\eqalign{ & \therefore \frac{1}{x} + \frac{1}{y} = \frac{{x + y}}{{xy}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{40}}{{275}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{8}{{75}} \cr} $$
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