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Question

The difference between two positive numbers x and y (x>y) is 4 and the difference between their reciprocals is 421. Then the numbers are

A
7,3
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B
8,4
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C
9,5
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D
10,6
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Solution

The correct option is A 7,3
According to the problem,

(xy)=4....................(1)

and
(1y1x=421)

(xyxy)=421

xy=214(xy)
xy=2144..................using (1)

xy=21

x(x4)=21...............From(1)

x24x21=0

(x+3)(x7)=0

Since x>0 then x=7.

Then y=3

The numbers are 7,3.

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