Question

A,B,C can do a piece of work in 2 hours.If B alone can do the same work in 80 hours, how long will A and C take to do it together?If C alone can do the work in 60 hours, how long will A take to do it alone?​

Answer 1

Answer:

A and C can do the same work in 80/39

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

Step-by-step 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