Question

A & B can do a piece of work in72 days, B&C can do the same work in 120 days, wheras A & C can do that work in 90 days, if A, B&C work together how much piece work they can finish after 3 days?

Answer 1

Answer :-

They all together complete the 20th part of the work in 3 days.

Step-by-step explanation:

A and B do a piece of work in 72 days.

So, work done by A and B in one day = $\sf{\frac{1}{72}}$

Similarly,

B and C do a piece of work in 120 days and A and C do that work in 90 days.

So,

Work done by B and C in one day = $\sf{\frac{1}{120}}$

And work done by A and C in one day = $\sf{\frac{1}{90}}$

We have to find the work done by A, B and C all together in 3 days.

Now,

$\sf{\bold{Work\:done\:by\:A,\:B\:and\:C\:all\:together\:=\:Work}}$ $\sf{\bold{done\:by\:A-B,\:B-C\:and\:C-A\:in\:1\:day}}$

=> $\sf{A\: +\: B\: + \:B \:+\: C \:+ C \:+ \:A\: = \:\frac{1}{72}\:+\:\frac{1}{120}\:+\:\frac{1}{90}}$

=> $\sf{2A\: +\:2 B\: + \: 2C \:=\:\frac{15\:+\:9\:+\:12}{1080}}$

=> $\sf{2(A\:+\:B\:+\:C)\:=\:\frac{36}{1080}}$

=> $\sf{A\:+\:B\:+\:C\:=\:\frac{1}{30(2)}}$

=> $\sf{A\:+\:B\:+\:C\:=\:\frac{1}{60}}$

•°• A, B and C together finish the work in 60 days.

But we have to find the work done by A, B and C all together in 3 days.

So, for 3 days :

Work done by A, B and C in 3 days = $\sf{\frac{60}{3}}$

= 20

•°• A, B and C together complete the 20th of the work in 3 days.

Answer 2

Answer:

A & B do work in = 72 days

Therefore, A & B do amount of work in one day =

$\frac{1}{72}$

B & C can do work in= 120 days

therefore, B & C do amount of work in one day =

$\frac{1}{120}$

A & C can do work in= 90 days

therefore, A & C do amount of work in one day =

$\frac{1}{90}$

Now, sum of the work done by all in one day,

- A + B = 1/72

- B + C = 1/120

- A + C = 1/90

- (A + B) + (B + C) + (A + C) = 1/72 + 1/120 + 1/90

- 2(A + B + C) =

$\frac{5 + 3 + 4}{360}$

- A + B + C =

$\frac{12}{360} \times \frac{1}{2}$

- A + B + C =

$\frac{12}{720}$

- A + B + C = 1/60

therefore, A, B & C can do 1/60 amount of work in one day.

If they work together, they can finish piece of work in 3 days =

$\frac{1}{60} \times 3$

$= \frac{1}{20}$

# hope this helps you.

#if you are satisfied with my answer then follow me and mark it as brainlliest.

# follow me

# mark as brainlliest.