Question

instead of calculating the sum of a proper fraction 1/2 with its reciprocal, the difference was worked out : as a reult of which there was an error of 121(39/41)%. what is the
fraction

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Answer 1

Given :- instead of calculating the sum of a proper fraction 1/2 with its reciprocal, the difference was worked out : as a reult of which there was an error of 121(39/41)%. what is the fraction ?

Solution :-

Let us assume that, the given proper fraction is (x/y) where y > x.

So,

→ Actual sum = (x/y) + (y/x). = (x² + y²)/xy

but,

→ calculated value = (x/y) - (y/x) = (x² - y²)/xy

So,

→ Error = Actual sum - calculated value = {(x² + y²)/xy} - {(x² - y²)/xy} = {(x² + y² - x² + y²) / xy} = 2y²/xy = (2y/x).

than,

→ % error = {2y/x) * 100 / [ (x² + y²)/xy ] = (200y * xy) / x(x² + y²) = (200y²/(x² + y²) %

given that, % error was 121(39/41) % .

therefore,

→ 200y²/(x² + y²) = 121(39/41)

→ 200y²/(x² + y²) = 5000/41

→ y²/(x² + y²) = 25/41

→ y²/(x² + y²) = 25 / (25 + 16)

→ y²/(x² + y²) = 5² / (5² + 4²)

comparing , we get,

→ y = 5.

→ x = 4.

Hence, Required Proper Fraction is = (4/5) (Ans.)

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