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A natural number when increased by 12 equals 160 times its reciprocal. Find the number?

Correct Answer: 8

Explanation:

Let the required number be 'p'.


From the given data,


p + 12 = 160 x 1/p


=> p + 12 = 160/p


=> p(p + 12) = 160


=> P^2 + 12p - 160 = 0


=> p^2 + 20p - 8p - 160 = 0


=> P(p + 20) - 8(p + 20) = 0


=> (p + 20)(p - 8) = 0


=> p = -20 or p = 8


As, given the number is a natural number, so it can't be negative.


Hence, the required number p = 8.


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