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Question

The sum of two numbers is 15. The sum of their reciprocals is 518. Find the numbers.


A

7 and 8

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B

9 and 6

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C

10 and 5

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D

11 and 4

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Solution

The correct option is B

9 and 6


Let the numbers be x and 15x

1x+115x=518

15x(15x)=518

54=15xx2

x215x+54=0

x29x6x+54=0

(x9)(x6)=0

x = 9, 6

Taking x = 9, 15x = 6

Taking x = 6, 15x = 9

Hence, two numbers are 9 and 6.


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