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On dividing $50$ into two parts such that the sum of their reciprocals is $\dfrac{1}{12}$, we get the parts as:

  1. $20,30$
  2. $24,26$
  3. $28,22$
  4. $36,14$
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use Option elimination technique,u will get A

2 Answers

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Answer: A (20, 30)

Lets say 50 divided into two parts x and 50-x.

Now, reciprocals are 1/x and 1/50-x

1/x + 1/(50-x)= 1/12

Solve, you’ll get x= 20 and 30.
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Let’s assume one part of 50 is $x$,then other will be $(50-x)$

Now according to the question sum of reciprocal is $\frac{1}{12}$

$\implies \frac{1}{x}+\frac{1}{(50-x)}=\frac{1}{12}$

$\implies \frac{50-x+x)}{x*(50-x)}=\frac{1}{12}$

$\implies 50*12=x*(50-x)$

$\implies 600=50x-x^2$

$\implies x^2-50x+600=0$

$\implies x^2-30x-20x+600=0$

$\implies x(x-30)-20(x-30)=0$

$\implies (x-30)(x-20)$

$\implies x=30,20$

Option (a) is correct.
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