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Question

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


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Solution

Step 1: Let the number is nand form the equation.

Know that, when the number is increased by 12, equals 160 times its reciprocal.

Therefore,

n+12=1n×160n2+12n=160n2+12n-160=0

Step 2: Solve the above quadratic equation.

n2+12n-160=0n2+20n-8n-160=0nn+20-8n+20=0n+20n-8=0n=-20,8

Since natural numbers cannot be negative.

Therefore n=8.

Hence the natural number when increased by 12, equals 160 times its reciprocal is 8.


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