Karanja and Ouma can do a certain job in 6 days. Karanja alone can do the work in 5 days more than Ouma. How many days can Karanja take to do the job alone?


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Question Number 72498 by Mr Jor last updated on 29/Oct/19

$K a r a n j a a n d O u m a c a n d o a$ $c e r t a i n j o b i n 6 d a y s . K a r a n j a$ $a l o n e c a n d o t h e w o r k i n 5 d a y s$ $m o r e t h a n O u m a . H o w m a n y$ $d a y s c a n K a r a n j a t a k e t o d o t h e$ $j o b a l o n e ?$
	Answered by Tanmay chaudhury last updated on 29/Oct/19

	$(K + O) p e r f o r m i n 1 d a y \frac{1}{6} p o r t i o n o f w o r k$ $l e t O c o m p l e t e s t h e w o r k i n x d a y s$ $s o O p e r f o r m i n 1 d a y s \frac{1}{x} p o r t i o n$ $l e t K c o m p l e t e s t h e w o r k i n (x + 5) d a y s$ $s o K p e r f o r m t h e w o r k i n 1 d a y s \frac{1}{x + 5} p o r t i o n$ $\frac{1}{x} + \frac{1}{x + 5} = \frac{1}{6}$ $\frac{x + 5 + x}{x^{2} + 5 x} = \frac{1}{6} \to x^{2} + 5 x = 12 x + 30$ $x^{2} - 7 x - 30 = 0$ $x^{2} - 10 x + 3 x - 30 = 0$ $x (x - 10) + 3 (x - 10) = 0$ $(x - 10) (x + 3) = 0$ $x \neq - 3 s o x = 10$ $s o O u m a c o m p l e t e t h e w o r k i n 10 d a y s$ $a n d K a r a n j a c o m p l e t d w o r k i n 15 d a y s$
	Commented by malwaan last updated on 30/Oct/19

	$v e r y n i c e!$
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