Question

12. A, B and C together complete a piece of work in 15 days. A and B complete the work in 20 days. A and C do the
same work in 30 days. In how many days, will
(i) B alone? (ii) C alone? (in) B and C together, complete the work?

Answer 1

Answer:

b alone 120days

c alone 60 days

b and c together 20 days

Answer 2

$\mathtt{\huge{\underline{\red{Answer\: :}}}}$

Given :

A + B + C = 15 days

A + B = 20 days

A + C = 30 days

According to the question :

A + B + C ' s 1 day work = 1 / 15

A + B ' s 1 day work = 1 / 20

A + C ' s 1 day work = 1 / 30.

Equations :

1 ) B = ( A + B + C ) - ( A + C )

☞ B = 1 / 15 - 1 / 30 ( LCM = 30 )

☞ B = 2 - 1 / 30

☞ B = 1 / 30

☞ B = 30 days

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2 ) C = ( A + B + C ) - ( A + B )

☞ C = 1 / 15 - 1 / 20 ( LCM = 60 )

☞ C = 4 - 3 / 60

☞ C = 1 / 60

☞ C = 60 days.

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3 ) If A + B can do the work in 20 days,

☞ B + C too will take the same time.

☞ so, B + C = 20 days .

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Therefore, B alone = 30

days, C alone = 60 days

and B + C together = 20

days .