A-and-B-can-do-a-work-in-12-days-and-17-days-respectively-and-with-the-help-of-C-they-complete-the-work-in-5-days-and-earn-Rs-238-Find-the-share-of-B-

Question Number 7705 by Obenfo last updated on 10/Sep/16

A and B can do a work in 12 days and

17 days respectively and with the help

of C they complete the work in 5 days

and earn Rs . 238 . Find the share of B .

Answered by Rasheed Soomro last updated on 10/Sep/16

A c a n d o a w o r k i n 12 d a y s

I n o n e d a y A c a n d o \frac{1}{12} o f w h o l e w o r k

I n 5 d a y s A c a n d o \frac{5}{12} o f w h o l e w o r k

B c a n d o t h e w o r k i n 17 d a y s

I n o n e d a y B c a n d o \frac{1}{17} o f w h o l e w o r k

I n 5 d a y s B c a n d o \frac{5}{17} o f w h o l e w o r k

I n 5 d a y s A, B & C c a n d o t h e w h o l e w o r k

L e t C h a s d o n e c o f w h o l e w o r k

\frac{5}{12} + \frac{5}{17} + c = 1 (w h o l e w o r k)

c = 1 - \frac{5}{12} - \frac{5}{17} = \frac{12 \times 17 - 5 \times 17 - 5 \times 12}{12 \times 17} = \frac{204 - 85 - 60}{204} = \frac{59}{204}

I n 5 d a y s w h o l e w o r k A, B a n d C h a s r e s p e c t i v e l y s h a r e d a s f o l l o w s

\frac{5}{12}, \frac{5}{17}, \frac{59}{204}

S o R s 238 w i l l b e s h a r e d

S h a r e o f A = 238 \times \frac{5}{12} = R s 99 \frac{1}{6}

S h a r e o f B = 238 \times \frac{5}{17} = R s 70

S h a r e o f A = 238 \times \frac{59}{204} = R s 68 \frac{5}{6}