A gets 1/5 of some amount, B gets 1/3 of remaining, C gets 1/6 of remaining, D gets 1/7 of remaining and E gets rest of amount. What fraction gets E ?


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Question Number 7881 by Rasheed Soomro last updated on 23/Sep/16
$A gets 1/5 of some amount, B gets 1/3 of remaining, C gets 1/6 of remaining, D gets 1/7 of remaining and E gets rest of amount. What fraction gets E ?$
$A g e t s 1 / 5 o f s o m e a m o u n t,$ $B g e t s 1 / 3 o f r e m a i n i n g, C$ $g e t s 1 / 6 o f r e m a i n i n g, D g e t s$ $1 / 7 o f r e m a i n i n g a n d E g e t s$ $r e s t o f a m o u n t . W h a t f r a c t i o n$ $g e t s E ?$
Commented by sandy_suhendra last updated on 23/Sep/16

$A = \frac{1}{5}$ $B = \frac{1}{3} [1 - \frac{1}{5}] = \frac{4}{15}$ $C = \frac{1}{6} [1 - \frac{1}{5} - \frac{4}{15}] = \frac{4}{45}$ $D = \frac{1}{7} [1 - \frac{1}{5} - \frac{4}{15} - \frac{4}{45}] = \frac{20}{315}$ $E = 1 - \frac{1}{5} - \frac{4}{15} - \frac{4}{45} - \frac{20}{315} = \frac{120}{315} = \frac{8}{21}$ $o r$ $A = \frac{1}{5} s o t h e r e m a i n i n g = 1 - \frac{1}{5} = \frac{4}{5}$ $B = \frac{1}{3} \times \frac{4}{5} = \frac{4}{15}$ $C = \frac{1}{6} \times \frac{4}{5} = \frac{2}{15}$ $D = \frac{1}{7} \times \frac{4}{5} = \frac{4}{35}$ $E = \frac{4}{5} - \frac{4}{15} - \frac{2}{15} - \frac{4}{35} = \frac{30}{105} = \frac{2}{7}$ $b u t I {d o n}^{'} t k n o w w h i c h o n e i s t r u e$
Commented by Rasheed Soomro last updated on 27/Sep/16
$I think your first answer is correct. I have done it slightly in defferent way. A gets (1/5) Remaining after A=1−(1/5)=(4/5) B gets (4/5)×(1/3)=(4/(15)) Remaining after B=(4/5)−(4/(15))=((12−4)/(15))=(8/(15)) C gets (8/(15))×(1/6)=(4/(45)) Remaining after C=(8/(15))−(4/(45))=((24−4)/(45))=((20)/(45))=(4/9) D gets (4/9)×(1/7)=(4/(63)) Remaining after D=(4/9)−(4/(63))=((28−4)/(63))=((24)/(63))=(8/(21)) E gets (8/(21))×1=(8/(21)) [ D gets whole of the remaining] E gets fraction (8/(21))$
$I t h i n k y o u r f i r s t a n s w e r i s c o r r e c t .$ $I h a v e d o n e i t s l i g h t l y i n d e f f e r e n t$ $w a y .$ $A g e t s \frac{1}{5}$ $R e m a i n i n g a f t e r A = 1 - \frac{1}{5} = \frac{4}{5}$ $B g e t s \frac{4}{5} \times \frac{1}{3} = \frac{4}{15}$ $R e m a i n i n g a f t e r B = \frac{4}{5} - \frac{4}{15} = \frac{12 - 4}{15} = \frac{8}{15}$ $C g e t s \frac{8}{15} \times \frac{1}{6} = \frac{4}{45}$ $R e m a i n i n g a f t e r C = \frac{8}{15} - \frac{4}{45} = \frac{24 - 4}{45} = \frac{20}{45} = \frac{4}{9}$ $D g e t s \frac{4}{9} \times \frac{1}{7} = \frac{4}{63}$ $R e m a i n i n g a f t e r D = \frac{4}{9} - \frac{4}{63} = \frac{28 - 4}{63} = \frac{24}{63} = \frac{8}{21}$ $E g e t s \frac{8}{21} \times 1 = \frac{8}{21} [D g e t s w h o l e o f t h e r e m a i n i n g]$ $E g e t s f r a c t i o n \frac{8}{21}$
	Answered by FilupSmith last updated on 23/Sep/16

	$T o t a l = 1$ $1 = \frac{1}{5} + (\frac{1}{5}) \frac{1}{3} + (\frac{1}{5} \times \frac{1}{3}) \frac{1}{6} + (\frac{1}{5} \times \frac{1}{3} \times \frac{1}{6} \times \frac{1}{7}) + E$ $1 = \frac{1}{5} + \frac{1}{15} + \frac{1}{90} + \frac{1}{540} + E$ $1 = \frac{88}{315} + E$ $E = \frac{227}{315}$ $I a m u n s u r e i f i a n s w e r e d c o r r e c t$
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