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Question

# The sum of reciprocals of two number is 1130 and difference of reciprocals of two is −130. Find the two numbers.

A
5 & 6
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B
3 & 2
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C
7 & 9
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D
11 & 13
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Solution

## The correct option is A 5 & 6Given, Let the numbers be x & y Reciprocal ⇒1x & 1y 1x+1y=11301x−1y=−130 Consider, a=1x; b=1y a+b=1130−−−(i)a−b=−130−−−(ii) Add (i) & (ii) a+b=1130a−b=−130–––––––––––– 2a=1130−130=1030=13∴a=16 Substitute value of a in (i) 16+b=1130b=1130−16=11−530=630=15 Now, x=1a=6 & y=1b=5 The numbers are 5 & 6

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