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-

Question Number 7881 by Rasheed Soomro last updated on 23/Sep/16

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 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