Divide Rs- 200 into two parts such that 1-3rd of the first and 1-2 of the second are equal-

Let one part be x and the other part be 200/x 1/3x = 1/2 ( 200/x ) [ given ] ⇒x/3 = 100/x ⇒ x^2 = 300 x = √(300) = 10√(3) 1^st ...

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Standard IX

Mathematics

Conversion of Recurring Decimals to Fractions

Divide Rs. 20...

Question

Divide Rs. 200 into two parts such that $\frac{1}{3} r d$ of the first and $\frac{1}{2}$ of the second are equal.

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Solution

Let one part be x and the other part be $\frac{200}{x}$
$\frac{1}{3} x = \frac{1}{2} (\frac{200}{x}) [g i v e n]$
$\Rightarrow \frac{x}{3} = \frac{100}{x}$ $\Rightarrow x^{2} = 300$
$x = \sqrt{300} = 10 \sqrt{3}$
$1^{s t} p a r t = x = 10 \sqrt{3},$ other part $= \frac{200}{x} = \frac{200}{10 \sqrt{3}} = \frac{20}{\sqrt{3}}$

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Divide Rs. 200 into two parts such that $\frac{1}{3} r d$ of the first and $\frac{1}{2}$ of the second are equal.