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Time and Work

A and B tog...

Question

$A$ and $B$ together can do a piece of work in $30$ days. $A$ having worked for $16$ days, $B$ finishes the remaining work alone in $44$ days. In how many days shall $B$ finish the whole work alone?

30

days

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40

days

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60

days

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70

days

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Solution

The correct option is B $60$ days
$L e t t h e t o t a l w o r k b e W .$
$L e t t h e s p e e d o f A i n d o i n g e n t i r e w o r k b e x w o r k / d a y$
$L e t t h e s p e e d o f B i n d o i n g e n t i r e w o r k b e y w o r k / d a y$
$∴ \frac{W}{x + y} = 30$
$∴$ $W = 30 x + 30 y . . . . . . . . . . . . (1)$
$W o r k d o n e b y A i n 16 d a y s = 16 x$
$R e m a i n i n g w o r k d o n e b y B i n 44 d a y s = 44 y$
$∴ 16 x + 44 y = W . . . . . . . . . (2)$
$F r o m (1) a n d (2), W = 60 y$
$H e n c e, i f B w o r k s a l o n e t h e n t h e w o r k w i l l b e c o m p l e t e d i n \frac{W}{y} d a y s = \frac{60 y}{y} d a y s = 60 d a y s .$

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A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?

$A$ and $B$ together can do a piece of work in $30$ days. $A$ having worked for $16$ days, $B$ finishes the remaining work alone in $44$ days. In how many days shall $B$ finish the whole work alone?