$A$ does $\frac{4}{5}$ th of work in $20$ days. He then calls in $B$ and they together finish the remaining work in $3$ days. How long $B$ alone would take to do the whole work ?

23

days

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37

days

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37 \frac{1}{2}

days

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40

days

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Solution

The correct option is B $37 \frac{1}{2}$ days
$L e t t h e t o t a l w o r k b e x .$
$∴ T h e s p e e d a t w h i c h a m o u n t o f w o r k A d o e s i n 20 d a y s i s = \frac{x}{25}$
$L e t t h e s p e e d o f B b e B w o r k p e r d a y .$
$S i n c e, t h e w o r k d o n e b y A i s \frac{4}{5} x$
$∴ R e m a i n i n g w o r k i s x - \frac{4}{5} x = \frac{x}{5}$
$I f A a n d B w o r k t o g e t h e r t h e n w e h a v e,$
$\frac{\frac{x}{5}}{\frac{x}{25} + B} = 3$
$∴ s p e e d o f B = \frac{2 x}{75} w o r k p e r d a y .$
$I f B a l o n e w o r k s t h e n t h e w o r k w i l l b e c o m p l e t e d i n \frac{x}{\frac{2 x}{75}} = 37 \frac{1}{2} d a y s .$

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