Question

ONE
7. A and B can paint the fence of a park in 8 days, B and C can paint the fence in 12 days and
C and A can paint the fence in 6 days. In how many days will (i) each one of them paint
the fence (ü) all of them working together paint the fence?
Co
(Hint: Work done by A in 1 day = Work done by all 3 in 1 day- work done by B+C in 1 day]​

Answer 1

Correct Question :

A and B can paint the fence of a park in 8 days, B and C can paint the fence in 12 days and  C and A can paint the fence in 6 days. In how many days will

( i ) each one of them paint  the fence

( ii ) all of them working together paint the fence?

[ Hint : Work done by A in 1 day = Work done by all 3 in 1 day- work done by B+C in 1 day ] ​

Step-by-step explanation:

A and B can paint the fence in 8 days

Work done by A and B in one day = A + B = 1 / 8 → ( 1 )

B and C can paint the fence in 12 days

Work done by B and C in one day = B + C = 1 / 12 → ( 2 )

C and A can do paint the fence in 6 days

Work done by C and A in one day = C + A = 1 / 6 → ( 3 )

Adding all 3 equations ( 1 ), ( 2 ) & ( 3 ) we get

⇒ 2( A + B + C ) = 1/8 + 1/12 + 1/6

⇒ 2( A + B + C ) = ( 3 + 2 + 4 ) / 24

⇒ 2( A + B + C ) = 9 / 24

⇒ 2( A + B + C ) = 3 / 8

⇒ A + B + C = 3 / 16

Work done by A, B, C in 1 day = A + B + C = 3 / 16

∴ A, B and C can paint the fence in 16/3 or 5.33 days

Work done by A in 1 day = Work done by all 3 in 1 day- work done by B + C in 1 day = 3/16 - 1/12 = ( 9 - 4 ) / 48 = 5/48

∴  A can paint the fence in 48/5 or 9.6 days

Work done by B in 1 day = Work done by all 3 in 1 day- work done by A+C in 1 day  = 3/16 - 1/6 = ( 9 - 8 ) / 48 = 1 / 48

∴  B can paint the fence in 48 days.

Work done by C in 1 day = Work done by all 3 in 1 day- work done by A + B in 1 day = 3/16 - 1/8 = ( 3 - 2 ) / 16 = 1 / 16

∴ C can paint the fence in 16 days.