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A natural number, when increased by 12, equals 160 times its reciprocal. Find the number. |
Answer» 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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