Question

a and b can do a piece of work in 72 days b and c can do it in 120 days a and c can do it in 90 days in what time can a b and c together finish the work​

Answer 1

A and B could complete work in 72 days

B and C could complete it in 90 days

C and A could complete it in 120 days

therefore,

work by a and b = 1/72

work by b and c = 1/90

work by a and c = 1/120

therfore work done by everyone

= 2(1/72+1/90+1/120)

= 2(5+4+3/360)

=2(12/360)

= 2(12/360)

= 2(1/60)

= 1/30

therefore the total days taken by a , b and c are 30 days....

Answer 2

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

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

• B and C can do it in 120 days.

• A and C can do it in 90 days.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• Time taken by A, B and C to finish the work together.

$\bf{\underline{\underline\green{Solution:-}}}$

$\rm A \: and \: B \: can \: do \: the \: work \: in \: 72 days$

$\rm (A \: and \: B)'s \: 1 \: day \: work = \dfrac{1}{72}$

$\rm B\: and \: C\: can \: do \:the \: work \: in \: 120 \: days$

$\rm (B \: and \: C)'s \: 1 \: day \: work = \dfrac{1}{120}$

$\rm A\: and \: C\: can \: do \:the \: work \: in \: 90\: days$

$\rm (A \: and \: C)'s \: 1 \: day \: work = \dfrac{1}{90}$

We have :-

$\rm\implies(A+ B) = \dfrac{1}{72}$

$\rm\implies(B+ C) = \dfrac{1}{120}$

$\rm\implies(A+ C) = \dfrac{1}{90}$

Now, we have to find the time taken by A, B and C together to do the work.

Adding all three:-

$\rm\implies(A+ B) + (B + C) + (C + A) = \dfrac{1}{72} + \dfrac{1}{120} + \dfrac{1}{90}$

$\rm\implies A+ B + B + C+ C + A = \dfrac{5+3+4}{360}$

$\rm\implies2A + 2B + 2C= \dfrac{12}{360}$

$\rm\implies2(A+ B+C)= \dfrac{1}{30}$

$\rm\implies(A+ B+C)= \dfrac{1}{30×2}$

$\rm\implies(A+ B+C)= \dfrac{1}{60}$

$\rm\implies(A+ B+C)'s \: \: 1 \: day \: work= \dfrac{1}{60}$

A + B + C can complete the work in 60 days.

$\large \underline{ \boxed{\rm \purple{A,B \: and \: C\: together \: can \: complete \: the \: work \: in \: 60 \: days}}}$