A natural number when increased by 11 becomes equal to 180 times its reciprocal. Find the number
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Answer:
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Step-by-step explanation:
Hi,
Let the natural number = c
If the number increased by 12 = x + 12
Reciprocal of the number = 1/x
According to the problem given,
x + 12 = 160 times of reciprocal of x
x + 12 = 160/ x
x( x + 12 ) = 160
x^2 + 12x - 160 = 0
x^2 + 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
But x is a natural number.
Therefore,
Required number = x = 8
I hope this helps you.
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