Question

ABC can do the piece of work in 2 hour if B alone can do the same work in 80 hour how long will a and c to take to do it together if C alone can do the work in 60 hours how long will a to take to do it​

Answer 1

Answer :-

A and C can do the same work in 80/39 i.e 2 2/39 hours.

A alone can do the same work in 240/113 i.e 2 14/113 hours

Explanation :-

ABC can the piece of work in 2 hours

So ABC's 1 hour work = 1/2

B alone can do the same work in 80 hours

So B's 1 hour work = 1/80

We know that

A and C 1 hour work = ABC 1 hour work - B's 1 hour work

= (1/2) - (1/80)

Taking LCM

= (40 - 1)/80

= 39/80

i.e A and C 1 hour work = 39/80

So A and C can do the same work in 80/39 i.e 2 2/39 hours.

C alone can do the same work in 60 hours

So C's 1 hours work = 1/60

We know that

A's 1 hour work = A and C 1 hour work - C's 1 hour work

= (39/80) - (1/60)

Taking LCM

= (117 - 4)/240

= 113/240

i.e A's 1 hour work = 113/240

So A alone can do the same work in 240/113 i.e 2 14/113 hours

Answer 2

$\LARGE \underline {\mathfrak{Solu} {\mathfrak{\green{tion:-}}}}$

ABC can do work in 2 hrs

⇒ ABC's 1 hr work = 1/2

A.T.Q,

Only B alone took 80 hrs to complete the work

⇒ B's 1 hr work = 1/80

A.T.Q,

(A and C)'s hr work = (ABC)'S 1 hr work - (B')s 1 hr work

______________[Put Values]

⇒ (1/2) - (1/80)

= (40 - 1)/80

= 39/80

So, (A and C)'s 1 hr work = 39/80

$\large{\bf{\star{\boxed{\boxed{\orange{(A \: and \:C) 's \: Work \: = \: 39/80}}}}}}$

_____________________

Time required = 80/39

Time = 2.051

Time ≈ 2 hrs

$\large{\bf{\star{\boxed{\boxed{\purple{Time \: taken \: by (A \: and \:C) 's \: Work \: ≈ \: 2hrs}}}}}}$

$\rule{200}{2}$

A.T.Q,

(A)'s 1 hr work = (A and C)'s 1 hr work - (C)'s 1 hr work

_______________[Put Values]

⇒ (39/80) - (1/60)

⇒ (117 - 4)/240

⇒ 113/240

So,

(A)'s 1hr work = 113/240

$\large{\bf{\star{\boxed{\boxed{\orange{(A) 's \: Work \: = \: 113/240}}}}}}$

________________________

Time Required = 240/113

Time = 2.12 hrs

Time ≈ 2 hrs

$\large{\bf{\star{\boxed{\boxed{\purple{Time \: Taken \: for(A) 's \: Work \: ≈ \: 2hrs}}}}}}$