Tow men complet a work in 3hr, three women complet it in 5hr, and five children complet it in 10hr. if we consider among these one man, one woman and one child in how much time they will complet it together?


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Question Number 215755 by Davidtim last updated on 17/Jan/25

$T o w m e n c o m p l e t a w o r k i n 3 h r, t h r e e$ $w o m e n c o m p l e t i t i n 5 h r, a n d f i v e$ $c h i l d r e n c o m p l e t i t i n 10 h r . i f w e c o n s i d e r$ $a m o n g t h e s e o n e m a n, o n e w o m a n a n d o n e$ $c h i l d i n h o w m u c h t i m e t h e y w i l l$ $c o m p l e t i t t o g e t h e r ?$
	Answered by A5T last updated on 17/Jan/25

	$One man completes \frac{1}{2 \times 3} = \frac{1}{6} of the work in 1 hr$ $One woman completes \frac{1}{3 \times 5} = \frac{1}{15} of the work in 1 hr$ $One child completes \frac{1}{5 \times 10} = \frac{1}{50} of the work in 1 hr$ $\Rightarrow One man, one woman and one child will$ $complete \frac{1}{6} + \frac{1}{15} + \frac{1}{50} = \frac{19}{75} of the work in 1 hr$ $\Rightarrow They complete in work in \frac{75}{19} hrs = 3 \frac{18}{19} hrs$
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