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Question
A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
Solution
Let the natural number = x
When the number increased by 12 = x + 12
Reciprocal of the number = `1/x`
According to the question, we have,
x + 12 = 160 times of reciprocal of x
x + 12 = `160/x`
x(x + 12) = 160
x2 + 12x – 160 = 0
x2 + 20x – 8x – 160 = 0
x(x + 20) – 8(x + 20) = 0
(x + 20)(x – 8) = 0
x + 20 = 0 or x – 8 = 0
x = – 20 or x = 8
Since, natural numbers cannot be negative.
The required number = x = 8
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