Question

A B and C working together can finish a piece of work in 8 hours a alone can do it in 20 hours and B alone can do it 24 hours in how many hours will see alone do the same work

Answer 1

Solution :-

Time taken by A, B and C working together to finish a work = 8 hours 

Work done by A, B and C working together in one hour = 1/8

Time taken by A alone to finish the work = 20 hours

Work done by A in 1 hour = 1/20 

Time taken by B alone to finish the work = 24 hours

Work done by B in 1 hour = 1/24

So, work done by C  = 1/8 - (1/20 + 1/24)

Taking LCM of the denominators and then solving it.

⇒ [15 - (6 + 5)]/120

⇒ (15 - 11)/120

⇒ 4/120

⇒ 1/30 

So, C alone can do the same work in 30 hours.

Answer 2

A, B & C working together to finish a work = 8 hours

In 1 hour Work done by A, B and C working together = 1/8

A alone can finish the work = 20 hours

In 1 hour Work done by A = 1/20

B alone to finish the work = 24 hours

In 1 hour Work done by B = 1/24

In 1 hour work done by C = 1/8 - (1/20 + 1/24)



=1/8-(6+5)/120)

= 1/8 - (11/120)


= ( (15 - 11)/120)

= 4/120

= 1/30

C alone can do the same work in 1÷ 1/30= 1× 30 = hours.

Hence, C alone can do the same work in 30 hours.
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